CPM Homework Help : PC Problem 12-40

Find the matrix associated with rotating counterclockwise through the given angle measure.

Hint:

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

$90°$
Step (a):
$\left(1, 0\right) → \left(0, 1\right)$
$\left(0, 1\right) → \left(−1, 0\right)$
$\left[ \begin{array} { c c } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} \right] \left[ \begin{array} { l l } { a } & { b } \\ { c } & { d } \end{array} \right] = \left[ \begin{array} { c c } { 0 } & { 1 } \\ { - 1 } & { 0 } \end{array} \right]$

$150°$
Step (b):
$\left. \begin{array} { l } { ( 1,0 ) \Rightarrow ( - \frac { \sqrt { 3 } } { 2 } , \frac { 1 } { 2 } ) } \\ { ( 0,1 ) \Rightarrow ( - \frac { 1 } { 2 } , - \frac { \sqrt { 3 } } { 2 } ) } \end{array} \right.$