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Linear Algebra

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Find the Angle of a Rotation, Given Standard Matrix

LINALG-NTV7B8

The standard matrix of (counter-clockwise) rotation by $\theta$ is:

$$\begin{pmatrix}\cfrac{1}{2}&\cfrac{\sqrt{3}}{2}\\\ -\cfrac{\sqrt{3}}{2}&\cfrac{1}{2}\end{pmatrix}$$

What is $\theta$?

A

$\cfrac{\pi}{3}$

B

$\cfrac{\pi}{6}$

C

$0$

D

$-\cfrac{\pi}{6}$

E

$-\cfrac{\pi}{3}$