Question

please help me with this question I have no idea how to solve it, thanks
Suppose T is a transformation from ℝ2 to ℝ2. Find the matrix A that induces T if T is rotation by 1/6π.

Answer 1

A rotation by $1/6\pi$ counterclockwise about the origin is given by the matrix $$\begin{pmatrix} \cos(1/6\pi) & -\sin(1/6\pi) \ \sin(1/6\pi) & \cos(1/6\pi) \end{pmatrix} = \begin{pmatrix} \frac{\sqrt{3}}{2} & -\frac{1}{2} \ \frac{1}{2} & \frac{\sqrt{3}}{2} \end{pmatrix}.$$Therefore, the matrix that induces $T$ is $\boxed{\begin{pmatrix} \frac{\sqrt{3}}{2} & -\frac{1}{2} \ \frac{1}{2} & \frac{\sqrt{3}}{2} \end{pmatrix}}$.