Question

rotate the vector \\( \langle 3,-2\
angle \\) \\( 90^{\circ} \\) degrees counterclockwise about the origin. \\( \langle \square, \square \
angle \\)

Explanation:

Step1: Recall rotation matrix

The rotation matrix for a \(90^{\circ}\) counter - clockwise rotation is \(

$$\begin{bmatrix}0&-1\\1&0\end{bmatrix}$$

\).

Step2: Apply matrix - vector multiplication

Given the vector \(

$$\begin{bmatrix}3\\-2\end{bmatrix}$$

\), multiply it by the rotation matrix:

$$
LATEXBLOCK2

LATEXBLOCK3
=
LATEXBLOCK4
=
LATEXBLOCK5
$$

Answer:

\(\langle2,3
angle\)