Rotate the given triangle \( 90^{\circ} \) counter-clockwise about the origin. \[ \left[\begin{array}{ccc} -1 & 2 & 2 \\ -1 & -1 & 3 \end{array}\right] \]

Step 1 ：Find the rotation matrix for \( 90^{\circ} \) counter-clockwise rotation: \[ R = \left[\begin{array}{cc} \cos(90^{\circ}) & -\sin(90^{\circ}) \\ \sin(90^{\circ}) & \cos(90^{\circ}) \end{array}\right] = \left[\begin{array}{cc} 0 & -1 \\ 1 & 0 \end{array}\right]. \]

Step 2 ：Multiply the rotation matrix by the given points: \[ R \cdot \left[\begin{array}{ccc} -1 & 2 & 2 \\ -1 & -1 & 3 \end{array}\right] = \left[\begin{array}{cc} 0 & -1 \\ 1 & 0 \end{array}\right] \cdot \left[\begin{array}{ccc} -1 & 2 & 2 \\ -1 & -1 & 3 \end{array}\right]. \]

Step 3 ：Compute the product: \[ \left[\begin{array}{ccc} 1 & 1 & -3 \\ -1 & 2 & 2 \end{array}\right]. \]