Matrix Composition: Reflection and Dilation
Consider a transformation in the coordinate plane that involves two sequential steps: first, reflect a generic point \((x,y)\) about the line \(y=x\), and then enlarge the reflected point by a scale factor of 2 centered at the origin. The overall transformation is a composition of the reflection and dilation transformations.
2D Rotation Matrix Representation
Express the 2D rotation transformation by an angle \(\theta\) about the origin in matrix form. Clearly write out the matrix with the appropriate trigonometric functions.