A zero tensor is a tensor with all entries equal to zero.

tensor.

velocity is contravariant tensor becasue displacement tensor is contravariant.

Stress is a tensor because it affects the datum plane. When this is affected and it changes, it is then considered a tensor.

I'm not entirely sure, but I think the tensor contraction over these two tensors should give back the identity. For example: If the resistivity tensor is a 2x2 matrix, then the conductivity tensor is the inverse of this matrix.