CPM Homework Help : PC3 Problem 9-102

Write the matrix associated with clockwise rotation through each of the given angle measures.

Hint:

Think about the points $(1, 0)$ and $(0, 1)$ . If you rotated them through the given angle, where would they end up?

$90^\circ$
Step (a):
$(1, 0) → (0, 1)$
$(0, 1) → (−1, 0)$
$\begin{bmatrix}a&b\\c&d\end{bmatrix}\begin{bmatrix}1&0\\0&1\end{bmatrix}=\begin{bmatrix}0&1\\-1&0\end{bmatrix}$

$150^\circ$
Step (b):
$(1, 0) \Rightarrow\left(-\frac{\sqrt{3}}{2},-\frac{1}{2}\right)$
$(1, 0) \Rightarrow\left(\frac{1}{2},-\frac{\sqrt{3}}{2}\right)$