What's the matrix that rotates vectors by \($\pi/6$\) counterclockwise?
\(R(\theta) = \begin{pmatrix}\cos(\theta) &-\sin(\theta)\\ \sin(\theta) &\cos(\theta) \end{pmatrix}\\ \text{rotates a vector by }\theta \text{ in the counter clockwise direction}\\ \text{I leave you to determine }R\left(\dfrac{\pi}{6}\right)\)
