### Instruction: Find the matrix that corresponds to rotating about the origin by an angle of $120^\circ$ counter-clockwise.### Response: We know that the matrix corresponding to a rotation of $\theta$ degrees counter-clockwise about the origin is $\begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}$.
So we just need to substitute $\theta = 120^\circ$ into the matrix to get $\begin{pmatrix} \cos120^\circ & -\sin120^\circ \\ \sin120^\circ & \cos120^\circ \end{pmatrix}$.