a. The piezocaloric effect is a second-rank tensor property. Assuming you have an orthorhombic material with lattice parameters in a, b, and c equal to 1, 2, and 3 angstroms, respectively, and where the piezocaloric values in m/K along the [100], [010], and [001] are respectively, 90, 42, and 18, write the matrix P that represents the piezocaloric effect for this material. b. Determine the value of the cosine of the angle between [100] and [420]. c. Determine the value of the piezocaloric effect for this material (in m/K) along the [420] direction.