Show that the formula \(d \mathbf{A}=d \boldsymbol{\theta} \times \mathbf{A}\) for the change in an inertial frame of a vector \(\mathbf{A}\) that is stationary in a rotating frame is still valid when \(\mathbf{A}\) is not perpendicular to \(\boldsymbol{\Omega}\) and when the tail of \(\mathbf{A}\) is not situated at the rotation axis.