Question

rotate the vector (0,2) 270° degrees clockwise about the origin.

Explanation:

Step1: Recall rotation matrix

The rotation matrix for a \(270^{\circ}\) clockwise rotation (which is equivalent to a \(90^{\circ}\) counter - clockwise rotation) is \(

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

\).

Step2: Apply matrix - vector multiplication

Given the vector \(

$$\begin{bmatrix}0\\2\end{bmatrix}$$

\), multiply it by the rotation matrix:

$$
LATEXBLOCK2

LATEXBLOCK3
=
LATEXBLOCK4
=
LATEXBLOCK5
$$

Answer:

\(\langle - 2,0
angle\)