Rotate the vector \( \langle 3,-2\rangle 90^{\circ} \) clockwise about the origin.
\( \langle[?],[]\rangle \)

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\[ \langle -2, -3\rangle \]

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Step 1 ：\( R = \begin{bmatrix} \cos{(-90^\circ)} & -\sin{(-90^\circ)} \\ \sin{(-90^\circ)} & \cos{(-90^\circ)} \end{bmatrix} \)

Step 2 ：\( R = \begin{bmatrix} \cos{(-90^\circ)} & \sin{90^\circ} \\ -\sin{90^\circ} & \cos{(-90^\circ)} \end{bmatrix} \)

Step 3 ：\( R = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix} \)

Step 4 ：\( R\cdot\langle 3,-2\rangle = \begin{bmatrix} 0 & 1 \\ -1 & 0 \end{bmatrix}\cdot\begin{bmatrix} 3 \\ -2 \end{bmatrix} = \begin{bmatrix} -2 \\ -3 \end{bmatrix} \)

Step 5 ：\[ \langle -2, -3\rangle \]

Rotate the vector \( \langle 3,-2\rangle 90^{\circ} \) clockwise about the origin.\( \langle[?],[]\rangle \)

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Rotate the vector \( \langle 3,-2\rangle 90^{\circ} \) clockwise about the origin.
\( \langle[?],[]\rangle \)