Wite down the 4 times 4 3d matrix to rotate by an angle

Question

1. Write down the 4 × 4 3D matrix to move by (x_m, y_m, z_m).

2. Write down the 4 × 4 3D matrix to rotate by an angle ? about the y-axis.

3. Write down the 4 × 4 3D matrix to scale an object by 50% in all directions.

4. Write the 2D rotation matrix that rotates by 90 degrees clockwise.

5. Write the matrix from Exercise 4 as a product of three shear matrices.

6. Find the inverse of the rigid body transformation:

where R is a 3 × 3 rotation matrix and t is a 3-vector.