Complexity Explorer Santa Fe Institute

Your progress is not being saved! Enroll now or log in to track your progress or submit homework.

Vector and Matrix Algebra

Lead instructor:

3.2 Geometric Transformations » Quiz #18 Solution

Question 1:

Recall that the matrix encoding a counter-clockwise rotation is given by: A_\theta=\begin{bmatrix} cos(\theta) & -sin(\theta) \\ sin(\theta) & cos(\theta) \end{bmatrix}

Consequently, A_{30}=\begin{bmatrix} cos(30) & -sin(30) \\ sin(30) & cos(30) \end{bmatrix} = \begin{bmatrix} \frac{\sqrt3}{2} & -\frac{1}{2} \\ \frac{1}{2} & \frac{\sqrt3}{2} \end{bmatrix}.