Composite Matrix Transformation: Reflection and Rotation
Consider the following sequence of transformations in the two-dimensional plane: (a) First, reflect a point \((x, y)\) about the line \(y=x\). (b) Then, rotate the reflected point about the origin by an angle \(\theta\) (in radians). For \(\theta = \frac{\pi}{4}\), determine the single matrix that represents the composite transformation.