Compute the transformation matrix for a lamina

Question

Response to the following problem:

Compute the transformation matrix for a lamina oriented at 45? with respect to the x-axis. Use it to find the transformed reduced stiffness matrix [Q] in laminate coordinates, corresponding to the reduced stiffness matrix [Q] in material coordinates computed in Problem 1.

Problem 1:

Compute the reduced stiffness [Q] and compliance [S] matrices, and the intralaminar shear stiffness [Q∗ ] and compliance [S ∗ ] matrices for a lamina with E₁ = 35 GP a, E₂ = 3.5 GP a, ν₁₂ = 0.3, G₁₂ = 1.75 GP a, G₂₃ = 0.35 GP a.