1. The problem is to represent an anticlockwise rotation of a matrix \( \begin{bmatrix} a & b \\ c & d \end{bmatrix} \). 2. A 2D anticlockwise rotation by an angle \(\theta\) is performed by multiplying the matrix by a rotation matrix \(R(\theta) = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix} \). 3. The rotated matrix is given by the product: $$ \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix} \begin{bmatrix} a & b \\ c & d \end{bmatrix} = \begin{bmatrix} a \cos \theta - c \sin \theta & b \cos \theta - d \sin \theta \\ a \sin \theta + c \cos \theta & b \sin \theta + d \cos \theta \end{bmatrix} $$ 4. Explanation: Each entry in the new matrix is computed by the dot product of the rotation matrix rows with the original matrix columns, effectively rotating the original matrix anticlockwise by the angle \(\theta\).