Solution
= Solution
For a constant orthogonal Cartesian coordinate change $x'_i=Q_{ij}x_j$, the <tensor component transformation law> gives
$$
\boxed{u'_i=Q_{ij}u_j,\qquad B'_{ij}=Q_{ip}Q_{jq}B_{pq},\qquad Q^TQ=I.}
$$
Repeated indices are summed. Each index of an ordinary Cartesian <tensor> contributes one factor of $Q$. A <pseudotensor> would have an additional determinant factor under an orientation-reversing transformation; the rules here concern ordinary tensors.