The piezocaloric effect is a second rank tensor property.Assuming you have an orthorhombic material with lattice parameters a = 2amstrong, b = 3amstrong c = 4amstrong respectively and where the piezocaloric values in m^3/k along the [100],[010] and [001] are respectively 15, 07, and 59

1. Write the matrix P that represent the piezocaloric effect of this material.
2. Determine the value of the cosine of the angle between [100] and [100]
3. Determine the value of the cosine of the angle between [010] and [100]
4. Determine the value of the cosine of the angle between [001] and [100]
5. Determine the value of the piezocaloric effect for the material in (m^3/k) along the [100] direction
6. Determine the normal to the (100) plane in the material
7. Determine the angle between the normal to the (100) plane in the material and the [153] direction in this material