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Diketahui vektor $\\vec{u}$, $\\vec{v}$, $\\vec{u}+\\var{a}\\vec{v}$, dan $\\vec{u}-\\var{a}\\vec{v}$ saling tegak lurus. 

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Nilai dari $\\dfrac{|\\vec{u}|}{|\\vec{v}|}$ adalah $\\ldots$.

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Diketahui vektor normal dari bidang $U$ adalah $\\vec{n_1}=[2,3,a]$ dan vektor normal dari bidang $V$ adalah $\\vec{n_2}=[3,-4,\\var{a}]$. Diketahui juga bahwa kedua bidang tersebut saling tegak lurus. Salah satu titik potong kedua bidang tersebut adalah $(\\var{b},\\var{c},4)$. 

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Pilihlah pernyataan yang tepat.

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Misal vektor voltase jantung berubah setelah jantung berdenyut mengikuti sistem persamaan beda $\\vec{v}_{t+1}=\\begin{bmatrix} 0&\\frac{1}{\\var{a}}\\\\ \\var{a}&0 \\end{bmatrix}\\vec{v}_t$.

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Salah satu solusi kesetimbangannya adalah $\\hat{v}=\\begin{bmatrix} a\\\\ b \\end{bmatrix}$ dengan $a$ dan $b$ bilangan asli. 

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Nilai minimum dari $a+b$ yang mungkin adalah $\\ldots$.

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Diberikan matriks $A=\\begin{bmatrix}
1&\\var{a} &\\var{b}\\\\
0&1&\\var{b}\\\\0&0&1
\\end{bmatrix}$. Perhatikan bahwa $A\\cdot A^T=I$. 

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Pernyataan berikut yang benar adalah $\\ldots$.

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Udang San Diego hidup di suatu empang yang penuh dan kering secara berkala setiap tahunnya. Saat empang tersebut kering, udang bertahan hidup menjadi kista. Populasinya dibagi menjadi tiga kelompok. Kista yang bertahan selama satu periode kering (1 DP) berada pada kelompok pertama, bertahan selama dua periode kering (2 DP) berada pada kelompok kedua, dan bertahan selama tiga periode kering (3 DP) berada pada kelompok ketiga. Diagram Leslie berikut menyajikan dinamik dari ketiga kelompok populasi berikut.

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Sebanyak $\\var{a}$ kista kelompok pertama berada pada empang.

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Banyaknya kista yang ada setelah periode kering pertama $240$. Nilai $a$ pada diagram tersebut adalah $\\ldots$.

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Perkiraan populasi udang kelompok pertama setelah dua periode kering pertama adalah $\\ldots$.

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Perkiraan populasi udang kelompok kedua setelah dua periode kering pertama adalah $\\ldots$.

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Waktunya 5 menit lagi ya.

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Selamat datang!

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Silakan gunakan set soal ini dengan bijak. Kalian bisa mencoba set soal ini terus-menerus.

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Set soal ini dapat digunakan oleh siapapun secara gratis.

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Petunjuk pengerjaan soal:

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Jika ada kunci jawaban yang salah, kalian dapat memberitahu kami di Instagram @meongmeongproject atau OA Line @eog7710d.

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