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Wajib.","2026-10-08T09:24:41.433Z",{"id":290,"subjectId":14,"levelId":48,"parentId":91,"slug":1448,"name":1449,"description":1450,"order":1451,"createdAt":1452,"updatedAt":1452},"matriks","Matriks","Matriks — Kelas 11 Lanjut.",13,"2026-10-08T09:24:41.441Z",{"id":1454,"subjectId":23,"levelId":48,"parentId":91,"slug":1455,"name":1456,"description":1457,"order":1451,"createdAt":1458,"updatedAt":1458},"cmuzbyhhz003k71r9s7s8evk1","rangkaian-pegas","Rangkaian Pegas","Rangkaian Pegas — Kelas 11.","2026-10-08T09:24:41.111Z",{"id":152,"subjectId":23,"levelId":48,"parentId":91,"slug":1460,"name":1461,"description":1462,"order":1463,"createdAt":1464,"updatedAt":1464},"fluida","Fluida","Fluida — Kelas 11.",14,"2026-10-08T09:24:41.113Z",{"id":266,"subjectId":14,"levelId":48,"parentId":91,"slug":1466,"name":1467,"description":1468,"order":1463,"createdAt":1469,"updatedAt":1469},"polinomial","Polinomial","Polinomial — Kelas 11 Lanjut.","2026-10-08T09:24:41.454Z",{"id":182,"subjectId":14,"levelId":48,"parentId":91,"slug":1471,"name":1472,"description":1473,"order":1474,"createdAt":1475,"updatedAt":1475},"fungsi-trigonometri","Fungsi Trigonometri","Fungsi Trigonometri — Kelas 11 Lanjut.",15,"2026-10-08T09:24:41.469Z",{"id":176,"subjectId":23,"levelId":48,"parentId":91,"slug":1477,"name":1478,"description":1479,"order":1474,"createdAt":1480,"updatedAt":1480},"gerak-harmonik-sederhana-ghs","Gerak Harmonik Sederhana (GHS)","Gerak Harmonik Sederhana (GHS) — Kelas 11.","2026-10-08T09:24:41.119Z",{"id":206,"subjectId":23,"levelId":48,"parentId":91,"slug":1482,"name":1483,"description":1484,"order":1485,"createdAt":1486,"updatedAt":1486},"gelombang-mekanik","Gelombang Mekanik","Gelombang Mekanik — Kelas 11.",16,"2026-10-08T09:24:41.132Z",{"id":272,"subjectId":14,"levelId":48,"parentId":91,"slug":1241,"name":1242,"description":1488,"order":1485,"createdAt":1489,"updatedAt":1489},"Vektor — Kelas 11 Lanjut.","2026-10-08T09:24:41.485Z",{"id":128,"subjectId":23,"levelId":48,"parentId":91,"slug":1491,"name":1492,"description":1493,"order":1494,"createdAt":1495,"updatedAt":1495},"gelombang-cahaya","Gelombang Cahaya","Gelombang Cahaya — Kelas 11.",17,"2026-10-08T09:24:41.150Z",{"id":212,"subjectId":14,"levelId":48,"parentId":91,"slug":1497,"name":1498,"description":1499,"order":1494,"createdAt":1500,"updatedAt":1500},"transformasi-geometri","Transformasi Geometri","Transformasi Geometri — Kelas 11 Lanjut.","2026-10-08T09:24:41.498Z",{"id":158,"subjectId":14,"levelId":48,"parentId":91,"slug":1502,"name":1503,"description":1504,"order":1505,"createdAt":1506,"updatedAt":1506},"fungsi-dan-pemodelannya","Fungsi dan Pemodelannya","Fungsi dan Pemodelannya — Kelas 11 Lanjut.",18,"2026-10-08T09:24:41.504Z",{"id":194,"subjectId":23,"levelId":48,"parentId":91,"slug":1508,"name":1509,"description":1510,"order":1505,"createdAt":1511,"updatedAt":1511},"optik","Optik","Optik — Kelas 11.","2026-10-08T09:24:41.161Z",{"id":68,"subjectId":14,"levelId":48,"parentId":91,"slug":1513,"name":76,"description":1514,"order":1515,"createdAt":1516,"updatedAt":1516},"barisan-dan-deret-kelas-12-wajib","Barisan dan Deret — Kelas 12 Wajib.",19,"2026-10-08T09:24:41.512Z",{"id":367,"subjectId":23,"levelId":48,"parentId":91,"slug":1518,"name":1519,"description":1520,"order":1515,"createdAt":1521,"updatedAt":1521},"suhu-dan-kalor","Suhu dan Kalor","Suhu dan Kalor — Kelas 11.","2026-10-08T09:24:41.169Z",{"id":98,"subjectId":14,"levelId":48,"parentId":91,"slug":1523,"name":1524,"description":1525,"order":1526,"createdAt":1527,"updatedAt":1527},"bunga","Bunga","Bunga — Kelas 12 Wajib.",20,"2026-10-08T09:24:41.518Z",{"id":164,"subjectId":23,"levelId":48,"parentId":91,"slug":1529,"name":1530,"description":1531,"order":1526,"createdAt":1532,"updatedAt":1532},"teori-kinetik-gas","Teori Kinetik Gas","Teori Kinetik Gas — Kelas 11.","2026-10-08T09:24:41.188Z",{"id":373,"subjectId":14,"levelId":48,"parentId":91,"slug":1534,"name":1535,"description":1536,"order":1537,"createdAt":1538,"updatedAt":1538},"investasi-dan-pinjaman","Investasi dan Pinjaman","Investasi dan Pinjaman — Kelas 12 Wajib.",21,"2026-10-08T09:24:41.525Z",{"id":391,"subjectId":23,"levelId":48,"parentId":91,"slug":1540,"name":1541,"description":1542,"order":1537,"createdAt":1543,"updatedAt":1543},"termodinamika","Termodinamika","Termodinamika — Kelas 11.","2026-10-08T09:24:41.202Z",{"id":319,"subjectId":14,"levelId":48,"parentId":91,"slug":1545,"name":1546,"description":1547,"order":1548,"createdAt":1549,"updatedAt":1549},"kaidah-pencacahan","Kaidah Pencacahan","Kaidah Pencacahan — Kelas 12 Wajib.",22,"2026-10-08T09:24:41.540Z",{"id":260,"subjectId":23,"levelId":48,"parentId":91,"slug":1551,"name":1552,"description":1553,"order":1548,"createdAt":1554,"updatedAt":1554},"listrik-statis","Listrik Statis","Listrik Statis — Kelas 12.","2026-10-08T09:24:41.215Z",{"id":230,"subjectId":23,"levelId":48,"parentId":91,"slug":1556,"name":1557,"description":1558,"order":1559,"createdAt":1560,"updatedAt":1560},"listrik-arus-searah","Listrik Arus Searah","Listrik Arus Searah — Kelas 12.",23,"2026-10-08T09:24:41.227Z",{"id":278,"subjectId":14,"levelId":48,"parentId":91,"slug":1562,"name":1411,"description":1563,"order":1559,"createdAt":1564,"updatedAt":1564},"peluang-kelas-12-wajib","Peluang — Kelas 12 Wajib.","2026-10-08T09:24:41.547Z",{"id":242,"subjectId":14,"levelId":48,"parentId":91,"slug":1566,"name":1567,"description":1568,"order":1569,"createdAt":1570,"updatedAt":1570},"geometri-analitik","Geometri Analitik","Geometri Analitik — Kelas 12 Lanjut.",24,"2026-10-08T09:24:41.553Z",{"id":236,"subjectId":23,"levelId":48,"parentId":91,"slug":1572,"name":1573,"description":1574,"order":1569,"createdAt":1575,"updatedAt":1575},"kemagnetan","Kemagnetan","Kemagnetan — Kelas 12.","2026-10-08T09:24:41.245Z",{"id":110,"subjectId":14,"levelId":48,"parentId":91,"slug":1577,"name":1578,"description":1579,"order":1580,"createdAt":1581,"updatedAt":1581},"limit","Limit","Limit — Kelas 12 Lanjut.",25,"2026-10-08T09:24:41.562Z",{"id":61,"subjectId":23,"levelId":48,"parentId":91,"slug":1583,"name":1584,"description":1585,"order":1580,"createdAt":1586,"updatedAt":1586},"listrik-ac-arus-bolak-balik","Listrik AC \u002F Arus Bolak Balik","Listrik AC \u002F Arus Bolak Balik — Kelas 12.","2026-10-08T09:24:41.263Z",{"id":301,"subjectId":23,"levelId":48,"parentId":91,"slug":1588,"name":1589,"description":1590,"order":1591,"createdAt":1592,"updatedAt":1592},"gelombang-elektromagnetik","Gelombang Elektromagnetik","Gelombang Elektromagnetik — Kelas 12.",26,"2026-10-08T09:24:41.273Z",{"id":116,"subjectId":14,"levelId":48,"parentId":91,"slug":1594,"name":1595,"description":1596,"order":1591,"createdAt":1597,"updatedAt":1597},"turunan-fungsi","Turunan Fungsi","Turunan Fungsi — Kelas 12 Lanjut.","2026-10-08T09:24:41.575Z",{"id":325,"subjectId":14,"levelId":48,"parentId":91,"slug":1599,"name":1600,"description":1601,"order":1602,"createdAt":1603,"updatedAt":1603},"aplikasi-turunan","Aplikasi Turunan","Aplikasi Turunan — Kelas 12 Lanjut.",27,"2026-10-08T09:24:41.587Z",{"id":355,"subjectId":23,"levelId":48,"parentId":91,"slug":1605,"name":1606,"description":1607,"order":1602,"createdAt":1608,"updatedAt":1608},"pengantar-instrumental-digital","Pengantar Instrumental Digital","Pengantar Instrumental Digital — Kelas 12.","2026-10-08T09:24:41.283Z",{"id":200,"subjectId":14,"levelId":48,"parentId":91,"slug":1610,"name":1611,"description":1612,"order":1613,"createdAt":1614,"updatedAt":1614},"integral","Integral","Integral — Kelas 12 Lanjut.",28,"2026-10-08T09:24:41.599Z",{"id":343,"subjectId":23,"levelId":48,"parentId":91,"slug":1616,"name":1617,"description":1618,"order":1613,"createdAt":1619,"updatedAt":1619},"relativitas-khusus","Relativitas Khusus","Relativitas Khusus — Kelas 12.","2026-10-08T09:24:41.291Z",{"id":349,"subjectId":23,"levelId":48,"parentId":91,"slug":1621,"name":1622,"description":1623,"order":1624,"createdAt":1625,"updatedAt":1625},"gejala-kuantum","Gejala Kuantum","Gejala Kuantum — Kelas 12.",29,"2026-10-08T09:24:41.303Z",{"id":248,"subjectId":14,"levelId":48,"parentId":91,"slug":1627,"name":1628,"description":1629,"order":1624,"createdAt":1630,"updatedAt":1630},"penerapan-integral","Penerapan Integral","Penerapan Integral — Kelas 12 Lanjut.","2026-10-08T09:24:41.607Z",{"id":140,"subjectId":14,"levelId":48,"parentId":91,"slug":1632,"name":1633,"description":1634,"order":1635,"createdAt":1636,"updatedAt":1636},"analisis-data-peluang","Analisis Data & Peluang","Analisis Data & Peluang — Kelas 12 Lanjut.",30,"2026-10-08T09:24:41.611Z",{"id":284,"subjectId":23,"levelId":48,"parentId":91,"slug":1638,"name":1639,"description":1640,"order":1635,"createdAt":1641,"updatedAt":1641},"fisika-inti-dan-radioaktivitas","Fisika Inti dan Radioaktivitas","Fisika Inti dan Radioaktivitas — Kelas 12.","2026-10-08T09:24:41.318Z",{"id":1643,"subjectId":14,"levelId":48,"parentId":91,"slug":1644,"name":1645,"description":1646,"order":1647,"createdAt":1648,"updatedAt":1648},"cmuzbyhw700gw71r9o87lq7vd","logaritma","Logaritma","Logaritma — Kelas 12 Lanjut.",31,"2026-10-08T09:24:41.623Z",{"id":1650,"subjectId":14,"levelId":48,"parentId":91,"slug":1651,"name":1652,"description":1653,"order":1654,"createdAt":1655,"updatedAt":1655},"cmuzbyhw900gy71r9d9sjh9ie","program-linier","Program Linier","Program Linier — Kelas 12 Lanjut.",32,"2026-10-08T09:24:41.625Z",{"id":1657,"subjectId":14,"levelId":48,"parentId":91,"slug":1658,"name":1659,"description":1660,"order":1661,"createdAt":1662,"updatedAt":1662},"cmuzbyhwb00h071r97764r7hr","bangun-ruang","Bangun Ruang","Bangun Ruang — Kelas 12 Lanjut.",33,"2026-10-08T09:24:41.627Z",{"id":1664,"subjectId":32,"levelId":91,"parentId":91,"slug":1665,"name":1666,"description":1667,"order":1668,"createdAt":1669,"updatedAt":1669},"demo-v2-topic-pemrograman-sd-1","demo-v2-sd-1","Algoritma: Urutan Perintah yang Jelas","Susun instruksi sederhana, lalu telusuri hasilnya selangkah demi selangkah.",100,"2026-10-08T10:03:56.954Z",{"id":1671,"subjectId":14,"levelId":48,"parentId":91,"slug":1672,"name":1673,"description":1674,"order":1668,"createdAt":1675,"updatedAt":1675},"demo-v2-topic-matematika-sma-1","demo-v2-sma-1","Fungsi kuadrat: akar, puncak, dan bentuk grafik","Menghubungkan bentuk umum, faktor, dan kuadrat sempurna untuk memahami parabola dan nilai optimum.","2026-10-08T10:03:56.485Z",{"id":1677,"subjectId":32,"levelId":48,"parentId":91,"slug":1672,"name":1678,"description":1679,"order":1668,"createdAt":1680,"updatedAt":1680},"demo-v2-topic-pemrograman-sma-1","Fungsi: Memisahkan Masukan, Proses, dan Hasil","Buat fungsi Python yang bisa dipakai ulang dan bedakan return dari print.","2026-10-08T10:03:57.108Z",{"id":1682,"subjectId":23,"levelId":42,"parentId":91,"slug":1683,"name":1684,"description":1685,"order":1668,"createdAt":1686,"updatedAt":1686},"demo-v2-topic-fisika-smp-1","demo-v2-smp-1","Gerak Lurus: Jarak, Perpindahan, dan Grafik Posisi","Membedakan kelajuan dan kecepatan rata-rata serta membaca arti kemiringan grafik posisi terhadap waktu.","2026-10-08T10:03:56.729Z",{"id":1688,"subjectId":23,"levelId":48,"parentId":91,"slug":1672,"name":1689,"description":1690,"order":1668,"createdAt":1691,"updatedAt":1691},"demo-v2-topic-fisika-sma-1","Hukum II Newton dan Gesekan pada Bidang Datar","Membuat diagram gaya, menentukan resultan, dan membedakan gesekan statis dari gesekan kinetik.","2026-10-08T10:03:56.801Z",{"id":1693,"subjectId":23,"levelId":91,"parentId":91,"slug":1665,"name":1694,"description":1695,"order":1668,"createdAt":1696,"updatedAt":1696},"demo-v2-topic-fisika-sd-1","Mengukur Panjang dan Volume Benda","Membaca penggaris, memakai satuan baku, dan menghitung isi kubus melalui susunan kubus kecil.","2026-10-08T10:03:56.657Z",{"id":1698,"subjectId":32,"levelId":53,"parentId":91,"slug":1699,"name":1700,"description":1701,"order":1668,"createdAt":1702,"updatedAt":1702},"demo-v2-topic-pemrograman-kuliah-1","demo-v2-kuliah-1","Pencarian Linear, Set, dan Biaya Operasi","Bandingkan cara mencari anggota data melalui langkah yang benar-benar dikerjakan.","2026-10-08T10:03:57.182Z",{"id":1704,"subjectId":14,"levelId":42,"parentId":91,"slug":1683,"name":1705,"description":1706,"order":1668,"createdAt":1707,"updatedAt":1707},"demo-v2-topic-matematika-smp-1","Perbandingan senilai dan berbalik nilai","Memilih model dari besaran yang tetap: rasio tetap untuk senilai dan hasil kali tetap untuk berbalik nilai.","2026-10-08T10:03:56.412Z",{"id":1709,"subjectId":14,"levelId":53,"parentId":91,"slug":1699,"name":1710,"description":1711,"order":1668,"createdAt":1712,"updatedAt":1712},"demo-v2-topic-matematika-kuliah-1","Turunan sebagai laju sesaat dan pendekatan lokal","Menurunkan fungsi dari limit hasil bagi selisih serta menghubungkan kemiringan, kecepatan, dan garis singgung.","2026-10-08T10:03:56.556Z",{"id":1714,"subjectId":32,"levelId":42,"parentId":91,"slug":1683,"name":1715,"description":1716,"order":1668,"createdAt":1717,"updatedAt":1717},"demo-v2-topic-pemrograman-smp-1","Variabel, Tipe Data, dan Keluaran Python","Simpan nilai dengan nama yang jelas dan bedakan angka dari teks.","2026-10-08T10:03:57.035Z",{"id":1719,"subjectId":23,"levelId":53,"parentId":91,"slug":1699,"name":1720,"description":1721,"order":1668,"createdAt":1722,"updatedAt":1722},"demo-v2-topic-fisika-kuliah-1","Vektor Tiga Dimensi dan Usaha sebagai Hasil Kali Titik","Menghubungkan komponen, panjang vektor, vektor satuan, proyeksi, dan makna fisik hasil kali titik.","2026-10-08T10:03:56.874Z",{"id":1724,"subjectId":14,"levelId":48,"parentId":91,"slug":1725,"name":1726,"description":1727,"order":1728,"createdAt":1729,"updatedAt":1729},"demo-v2-topic-matematika-sma-2","demo-v2-sma-2","Eksponen dan logaritma: mencari pangkat yang belum diketahui","Membedakan kenaikan tetap dan faktor tetap, lalu membaca logaritma sebagai operasi balik eksponen.",101,"2026-10-08T10:03:56.507Z",{"id":1731,"subjectId":14,"levelId":42,"parentId":91,"slug":1732,"name":1733,"description":1734,"order":1728,"createdAt":1735,"updatedAt":1735},"demo-v2-topic-matematika-smp-2","demo-v2-smp-2","Fungsi linear: gradien dan titik potong","Membaca y = mx + b sebagai perubahan tetap, menghitung gradien dari dua titik, dan memeriksa grafik.","2026-10-08T10:03:56.434Z",{"id":1737,"subjectId":23,"levelId":91,"parentId":91,"slug":1738,"name":1739,"description":1740,"order":1728,"createdAt":1741,"updatedAt":1741},"demo-v2-topic-fisika-sd-2","demo-v2-sd-2","Gaya: Dorongan, Tarikan, dan Perubahan Gerak","Mengenali siapa yang memberikan gaya, arah gaya, dan perubahan gerak atau bentuk yang dapat diamati.","2026-10-08T10:03:56.679Z",{"id":1743,"subjectId":23,"levelId":48,"parentId":91,"slug":1725,"name":1744,"description":1745,"order":1728,"createdAt":1746,"updatedAt":1746},"demo-v2-topic-fisika-sma-2","Gerak Peluru: Dua Arah dengan Satu Waktu","Menguraikan kecepatan awal, menghitung waktu terbang, tinggi maksimum, dan jangkauan untuk model ideal.","2026-10-08T10:03:56.824Z",{"id":1748,"subjectId":14,"levelId":53,"parentId":91,"slug":1749,"name":1750,"description":1751,"order":1728,"createdAt":1752,"updatedAt":1752},"demo-v2-topic-matematika-kuliah-2","demo-v2-kuliah-2","Integral tentu: akumulasi dan luas bertanda","Menghubungkan jumlah Riemann, antiturunan, dan teorema dasar kalkulus tanpa menyamakan perpindahan dengan jarak.","2026-10-08T10:03:56.578Z",{"id":1754,"subjectId":32,"levelId":53,"parentId":91,"slug":1749,"name":1755,"description":1756,"order":1728,"createdAt":1757,"updatedAt":1757},"demo-v2-topic-pemrograman-kuliah-2","Kelas dan Invarian pada Objek","Kelola keadaan dan perilaku bersama, lalu jaga agar objek selalu valid.","2026-10-08T10:03:57.206Z",{"id":1759,"subjectId":32,"levelId":48,"parentId":91,"slug":1725,"name":1760,"description":1761,"order":1728,"createdAt":1762,"updatedAt":1762},"demo-v2-topic-pemrograman-sma-2","List dan Dictionary untuk Mengolah Data","Pilih struktur data sesuai cara mengaksesnya dan hitung ringkasan data.","2026-10-08T10:03:57.131Z",{"id":1764,"subjectId":23,"levelId":42,"parentId":91,"slug":1732,"name":1765,"description":1766,"order":1728,"createdAt":1767,"updatedAt":1767},"demo-v2-topic-fisika-smp-2","Massa Jenis: Menghubungkan Massa dan Volume","Menghitung massa jenis, mengukur volume dengan perpindahan air, dan menjaga konsistensi satuan.","2026-10-08T10:03:56.750Z",{"id":1769,"subjectId":23,"levelId":53,"parentId":91,"slug":1749,"name":1770,"description":1771,"order":1728,"createdAt":1772,"updatedAt":1772},"demo-v2-topic-fisika-kuliah-2","Osilasi Harmonik Sederhana: Fase, Turunan, dan Energi","Menganalisis model x = A cos(ωt), menurunkan kecepatan dan percepatan, serta memeriksa kekekalan energi.","2026-10-08T10:03:56.896Z",{"id":1774,"subjectId":32,"levelId":91,"parentId":91,"slug":1738,"name":1775,"description":1776,"order":1728,"createdAt":1777,"updatedAt":1777},"demo-v2-topic-pemrograman-sd-2","Pengulangan: Langkah yang Dikerjakan Berkali-kali","Kenali pola berulang dan hitung hasil tiap putaran tanpa kehilangan jejak.","2026-10-08T10:03:56.978Z",{"id":1779,"subjectId":32,"levelId":42,"parentId":91,"slug":1732,"name":1780,"description":1781,"order":1728,"createdAt":1782,"updatedAt":1782},"demo-v2-topic-pemrograman-smp-2","Percabangan Python dan Batas Keputusan","Tulis if, elif, dan else serta uji nilai di sekitar batas.","2026-10-08T10:03:57.057Z",{"id":1784,"subjectId":23,"levelId":48,"parentId":91,"slug":1785,"name":1786,"description":1787,"order":1788,"createdAt":1789,"updatedAt":1789},"demo-v2-topic-fisika-sma-3","demo-v2-sma-3","Hukum Ohm, Daya, dan Energi pada Resistor","Menghubungkan tegangan, arus, hambatan, dan energi listrik tanpa mencampurkan satuan volt, ampere, watt, dan joule.",102,"2026-10-08T10:03:56.846Z",{"id":1791,"subjectId":32,"levelId":48,"parentId":91,"slug":1785,"name":1792,"description":1793,"order":1788,"createdAt":1794,"updatedAt":1794},"demo-v2-topic-pemrograman-sma-3","Membaca Berkas dan Menangani Masukan Salah","Ubah baris teks menjadi angka dan tangani kesalahan yang bisa diperkirakan.","2026-10-08T10:03:57.153Z",{"id":1796,"subjectId":14,"levelId":48,"parentId":91,"slug":1785,"name":1797,"description":1798,"order":1788,"createdAt":1799,"updatedAt":1799},"demo-v2-topic-matematika-sma-3","Peluang: ruang sampel, kejadian, dan pengambilan bertahap","Menghitung peluang melalui hasil yang sama mungkin dan memahami pengaruh pengembalian pada pengambilan kedua.","2026-10-08T10:03:56.528Z",{"id":1801,"subjectId":32,"levelId":53,"parentId":91,"slug":1802,"name":1803,"description":1804,"order":1788,"createdAt":1805,"updatedAt":1805},"demo-v2-topic-pemrograman-kuliah-3","demo-v2-kuliah-3","Pengujian Otomatis dan Kasus Batas","Uji kontrak fungsi dengan contoh biasa, batas, dan masukan tidak sah.","2026-10-08T10:03:57.229Z",{"id":1807,"subjectId":32,"levelId":91,"parentId":91,"slug":1808,"name":1809,"description":1810,"order":1788,"createdAt":1811,"updatedAt":1811},"demo-v2-topic-pemrograman-sd-3","demo-v2-sd-3","Percabangan: Memilih Tindakan dengan Syarat","Gunakan pertanyaan ya atau tidak untuk menentukan tindakan yang tepat.","2026-10-08T10:03:57.006Z",{"id":1813,"subjectId":32,"levelId":42,"parentId":91,"slug":1814,"name":1815,"description":1816,"order":1788,"createdAt":1817,"updatedAt":1817},"demo-v2-topic-pemrograman-smp-3","demo-v2-smp-3","Perulangan for dan Akumulator","Hitung total data dengan jejak putaran yang dapat diperiksa.","2026-10-08T10:03:57.079Z",{"id":1819,"subjectId":23,"levelId":91,"parentId":91,"slug":1808,"name":1820,"description":1821,"order":1788,"createdAt":1822,"updatedAt":1822},"demo-v2-topic-fisika-sd-3","Suhu dan Perpindahan Kalor di Sekitar Kita","Membaca perubahan suhu dan membedakan konduksi, konveksi, serta radiasi melalui kejadian sehari-hari.","2026-10-08T10:03:56.700Z",{"id":1824,"subjectId":14,"levelId":42,"parentId":91,"slug":1814,"name":1825,"description":1826,"order":1788,"createdAt":1827,"updatedAt":1827},"demo-v2-topic-matematika-smp-3","Teorema Pythagoras dan jarak diagonal","Menentukan sisi segitiga siku-siku dengan kuadrat panjang, lalu memeriksa hasil melalui geometri dan satuan.","2026-10-08T10:03:56.456Z",{"id":1829,"subjectId":23,"levelId":53,"parentId":91,"slug":1802,"name":1830,"description":1831,"order":1788,"createdAt":1832,"updatedAt":1832},"demo-v2-topic-fisika-kuliah-3","Usaha Gaya Berubah: Integral dan Teorema Energi Kinetik","Menghitung luas bertanda di bawah grafik gaya, menghubungkannya dengan integral, dan menentukan kelajuan akhir.","2026-10-08T10:03:56.918Z",{"id":1834,"subjectId":23,"levelId":42,"parentId":91,"slug":1814,"name":1835,"description":1836,"order":1788,"createdAt":1837,"updatedAt":1837},"demo-v2-topic-fisika-smp-3","Usaha dan Energi: Memeriksa Perubahan dengan Joule","Menghitung usaha gaya searah atau berlawanan, energi gerak, dan perubahan energi ketika benda diangkat.","2026-10-08T10:03:56.772Z",{"id":1839,"subjectId":14,"levelId":53,"parentId":91,"slug":1802,"name":1840,"description":1841,"order":1788,"createdAt":1842,"updatedAt":1842},"demo-v2-topic-matematika-kuliah-3","Vektor tiga dimensi dan hasil kali titik","Membaca komponen, menghitung panjang dan sudut, serta menafsirkan hasil kali titik sebagai keselarasan arah.","2026-10-08T10:03:56.615Z",[],{"id":1845,"type":1846,"slug":1847,"title":1720,"excerpt":1721,"coverUrl":91,"status":1848,"publishedAt":1849,"featured":5,"subjectId":23,"blocks":1850,"seoTitle":91,"seoDescription":91,"readingMinutes":57,"order":20,"createdAt":1904,"updatedAt":1904,"subject":1905,"levels":1906,"topics":1908,"tags":1910,"author":91,"resolved":1911,"related":1929},"demo-v2-m-fisika-kuliah-1","MATERIAL","demo-materi-fisika-kuliah-1","PUBLISHED","2026-10-08T10:03:56.890Z",[1851,1856,1860,1864,1871,1878,1882,1886,1890,1894,1898],{"id":1852,"data":1853,"type":1855},"section-1",{"markdown":1854},"## Tujuan dan prasyarat\n\nKamu akan menentukan panjang vektor tiga dimensi, membentuk vektor satuan, menghitung hasil kali titik, dan menggunakannya untuk usaha gaya konstan. Prasyaratnya adalah koordinat Kartesius, teorema Pythagoras, sinus–kosinus, serta definisi usaha. Kita memakai basis ortonormal: tiga arah sumbu saling tegak lurus dan setiap vektor basis panjangnya satu. Gaya dan perpindahan ditulis dalam kerangka yang sama.\n","text",{"id":1857,"data":1858,"type":1855},"section-2",{"markdown":1859},"## Komponen bukan panjang vektor\n\nVektor $\\vec r=(r_x,r_y,r_z)$ mempunyai tiga komponen. Untuk perpindahan, setiap komponen bersatuan meter. Bentuk $\\vec r=r_x\\hat i+r_y\\hat j+r_z\\hat k$ memakai vektor satuan basis, yang menyatakan arah sumbu x, y, dan z. Panjang vektor, ditulis $|\\vec r|$, adalah $\\sqrt{r_x^2+r_y^2+r_z^2}$. Kita mengkuadratkan komponen karena ketiga arah tegak lurus; menjumlahkan komponen biasa tidak memberi panjang.\n\nVektor satuan searah $\\vec r$ ialah $\\hat r=\\vec r\u002F|\\vec r|$ untuk vektor yang tidak nol. Komponennya tanpa satuan karena panjang dibagi panjang. Vektor satuan membantu memisahkan besar dari arah: $\\vec r=|\\vec r|\\hat r$. Vektor nol tidak mempunyai arah tunggal, sehingga normalisasi vektor nol tidak terdefinisi.\n",{"id":1861,"data":1862,"type":1855},"section-3",{"markdown":1863},"## Hasil kali titik sebagai ukuran keselarasan\n\nHasil kali titik adalah $\\vec A\\cdot\\vec B=A_xB_x+A_yB_y+A_zB_z=|\\vec A||\\vec B|\\cos\\theta$. Sudut $\\theta$ adalah sudut antara kedua vektor. Hasilnya skalar, dengan satuan hasil kali satuan A dan B. Nilai positif menunjukkan komponen searah yang dominan, nol menunjukkan tegak lurus untuk dua vektor tidak nol, dan negatif menunjukkan sudut tumpul.\n\nProyeksi skalar $\\vec A$ sepanjang arah satuan $\\hat u$ adalah $\\vec A\\cdot\\hat u$. Proyeksi vektornya adalah $(\\vec A\\cdot\\hat u)\\hat u$. Bedakan angka bertanda pada proyeksi skalar dari panah pada proyeksi vektor. Mengubah sudut kamera tidak mengubah vektor fisik; rotasi pandangan hanya membantu melihat hubungan ruang. Bahkan jika basis benar-benar diputar secara ortogonal, panjang dan hasil kali titik tetap sama, walaupun angka komponen dapat berubah.\n",{"id":1865,"data":1866,"type":1870},"visual-guide",{"title":1867,"variant":1868,"markdown":1869},"Eksplorasi visual","info","Kenali sumbu positif x merah, y hijau, dan z biru, masing-masing panjang 3 satuan, serta vektor oranye (1,2,2). Putar pandangan untuk melihat komponen pada tiga arah. Hitung panjang √(1²+2²+2²) = 3 satuan. Anggap satu satuan mewakili satu meter untuk latihan perpindahan. Kamera tidak mengubah komponen model. Dengan F = (4,−1,2) N, hitung usaha 6 J pada perpindahan tersebut; visual tidak menampilkan panah gaya tambahan.","callout",{"id":1872,"data":1873,"type":1877},"visual",{"height":1874,"assetId":1875,"caption":1876},480,"demo-v2-asset-vector","Vektor (1, 2, 2) dalam ruang","interactive",{"id":1879,"data":1880,"type":1855},"section-4",{"markdown":1881},"## Contoh 1: vektor pada visual\n\nAnggap panah oranye mewakili perpindahan $\\vec r=(1,2,2)$ m. Panjangnya $\\sqrt{1+4+4}=3$ m. Maka $\\hat r=(1\u002F3,2\u002F3,2\u002F3)$, tanpa satuan. Cek normalisasi: $(1\u002F3)^2+(2\u002F3)^2+(2\u002F3)^2=1$. Sudut terhadap sumbu x positif memenuhi $\\cos\\alpha=1\u002F3$, sehingga sekitar 70,53°. Terhadap y dan z positif, kosinusnya 2\u002F3 dan sudutnya masing-masing sekitar 48,19°. Ketiga sudut ini bukan sudut interior segitiga dan tidak harus berjumlah 180°.\n",{"id":1883,"data":1884,"type":1855},"section-5",{"markdown":1885},"## Contoh 2: usaha dalam ruang\n\nGaya konstan $\\vec F=(4,-1,2)$ N memindahkan benda sebesar $\\Delta\\vec r=(1,2,2)$ m. Hitung $W=\\vec F\\cdot\\Delta\\vec r=4(1)+(-1)(2)+2(2)=6$ J. Komponen y memberi −2 J karena gaya dan perpindahan di arah itu berlawanan. Cek menggunakan proyeksi: gaya sepanjang arah perpindahan adalah $\\vec F\\cdot\\hat r=2$ N, lalu $W=2(3)=6$ J. Panjang gaya $\\sqrt{21}$ N, sehingga $\\cos\\theta=6\u002F(3\\sqrt{21})\\approx0{,}436$ dan sudut sekitar 64,12°, konsisten dengan usaha positif.\n",{"id":1887,"data":1888,"type":1855},"section-6",{"markdown":1889},"## Batas penerapan dan kekeliruan\n\nRumus usaha hasil kali titik ini memakai gaya konstan sepanjang perpindahan. Jika gaya berubah, gunakan integral garis, bukan mengganti gaya dengan nilai akhir tanpa alasan. Hasil kali titik berbeda dari hasil kali silang; usaha adalah skalar, sedangkan torsi merupakan vektor. Hasil kali titik nol juga dapat disebabkan salah satu vektor nol, jadi jangan langsung menyimpulkan sudut 90° tanpa memeriksa kedua panjang.\n",{"id":1891,"data":1892,"type":1855},"section-7",{"markdown":1893},"## Ringkasan dan cek mandiri\n\nPanjang berasal dari jumlah kuadrat; arah satuan berasal dari pembagian oleh panjang. Hasil kali titik memilih komponen sepanjang arah lain. Untuk gaya (2,0,0) N dan perpindahan (0,3,0) m, usaha nol walaupun kedua vektor tidak nol. Jelaskan geometrinya, lalu periksa bahwa satuan N·m tetap bermakna joule meskipun nilai numeriknya nol.",{"id":1895,"data":1896,"type":1855},"sources",{"markdown":1897},"## Sumber belajar\n\n- [OpenStax University Physics Volume 1 — Products of Vectors](https:\u002F\u002Fopenstax.org\u002Fbooks\u002Funiversity-physics-volume-1\u002Fpages\u002F2-4-products-of-vectors)\n\nPenjelasan dan contoh disusun ulang untuk materi ini; sumber dapat dibuka untuk belajar lebih lanjut.",{"id":1899,"data":1900,"type":1903},"practice",{"title":1901,"questionSetId":1902},"Cek pemahaman: Vektor Tiga Dimensi dan Usaha sebagai Hasil Kali Titik","demo-v2-p-fisika-kuliah-1","quiz","2026-10-08T10:03:56.891Z",{"id":23,"slug":24,"name":25,"color":28,"icon":27},[1907],{"id":53,"slug":54,"name":55},[1909],{"id":1719,"slug":1699,"name":1720,"subjectId":23},[],{"assets":1912,"videos":1922,"questionSets":1923},{"demo-v2-asset-vector":1913},{"id":1875,"slug":1914,"kind":1915,"title":1876,"description":1916,"url":1917,"posterUrl":91,"config":1918,"subject":1921},"demo-vector","MODEL_3D","Sumbu x merah, y hijau, z biru; panah jingga dari titik asal ke (1, 2, 2), panjang 3 satuan. Sumbu positif panjang 3 satuan.","https:\u002F\u002Fmyfismat.com\u002Fuploads\u002Fdemo-v2-vector.glb",{"exposure":29,"enablePan":5,"autoRotate":4,"background":1919,"cameraOrbit":1920,"shadowIntensity":29},"#eef4ff","35deg 65deg 105%",{"id":14,"slug":15,"name":16},{},{"demo-v2-p-fisika-kuliah-1":1924},{"id":1902,"slug":1925,"title":1926,"mode":1927,"description":1928,"questionCount":57,"durationMinutes":91},"demo-latihan-fisika-kuliah-1","Latihan: Vektor Tiga Dimensi dan Usaha sebagai Hasil Kali Titik","PRACTICE","Tiga soal Fisika Kuliah dengan penalaran, langkah hitung, dan pembahasan pilihan yang keliru.",[1930,1945,1956,1967],{"id":1931,"type":1932,"slug":1933,"title":1934,"excerpt":1935,"coverUrl":91,"status":1848,"publishedAt":1936,"featured":5,"readingMinutes":1109,"order":20,"updatedAt":1937,"subject":1938,"levels":1939,"topics":1943,"tags":1944},"demo-v2-a-fisika","ARTICLE","demo-artikel-fisika","Belajar Fisika dari Pengamatan ke Model","Panduan menyusun pertanyaan, mencatat satuan, menguji prediksi, dan membaca perbedaan antara model ideal dengan pengukuran nyata.","2026-10-08T10:03:56.946Z","2026-10-08T10:03:56.948Z",{"id":23,"slug":24,"name":25,"color":28,"icon":27},[1940,1941,1942],{"id":42,"slug":43,"name":44},{"id":48,"slug":49,"name":50},{"id":53,"slug":54,"name":55},[],[],{"id":1946,"type":1846,"slug":1947,"title":1830,"excerpt":1831,"coverUrl":91,"status":1848,"publishedAt":1948,"featured":4,"readingMinutes":57,"order":38,"updatedAt":1949,"subject":1950,"levels":1951,"topics":1953,"tags":1955},"demo-v2-m-fisika-kuliah-3","demo-materi-fisika-kuliah-3","2026-10-08T10:03:56.934Z","2026-10-08T10:03:56.935Z",{"id":23,"slug":24,"name":25,"color":28,"icon":27},[1952],{"id":53,"slug":54,"name":55},[1954],{"id":1829,"slug":1802,"name":1830,"subjectId":23},[],{"id":1957,"type":1846,"slug":1958,"title":1770,"excerpt":1771,"coverUrl":91,"status":1848,"publishedAt":1959,"featured":4,"readingMinutes":57,"order":29,"updatedAt":1960,"subject":1961,"levels":1962,"topics":1964,"tags":1966},"demo-v2-m-fisika-kuliah-2","demo-materi-fisika-kuliah-2","2026-10-08T10:03:56.912Z","2026-10-08T10:03:56.913Z",{"id":23,"slug":24,"name":25,"color":28,"icon":27},[1963],{"id":53,"slug":54,"name":55},[1965],{"id":1769,"slug":1749,"name":1770,"subjectId":23},[],{"id":1968,"type":1846,"slug":1969,"title":1786,"excerpt":1787,"coverUrl":91,"status":1848,"publishedAt":1970,"featured":4,"readingMinutes":57,"order":38,"updatedAt":1971,"subject":1972,"levels":1973,"topics":1975,"tags":1977},"demo-v2-m-fisika-sma-3","demo-materi-fisika-sma-3","2026-10-08T10:03:56.861Z","2026-10-08T10:03:56.862Z",{"id":23,"slug":24,"name":25,"color":28,"icon":27},[1974],{"id":48,"slug":49,"name":50},[1976],{"id":1784,"slug":1785,"name":1786,"subjectId":23},[]]