(1). Consider a unit cube [0, 1]3 subject to the motion x = 4(X, t) = A(t)X + b(t), where in the right-hand orthonormal basis e1, e2, e3, at +1 at 0 t [Au] = 0 1 0 {bj} = t 1 O O Here, X = Xe; is the material coordinates, t 2 0 is the time, and a 2 0. . Determine the inverse motion (x, t). . Determine the displacement x - X in both Lagrangian and Eulerian coordinates, i.e., U(X, t) and u(x, t). . Determine the velocity in both Lagrangian and Eulerian coordinate, i.e., V(X, t) and v (x, t). . Determine the acceleration in both Lagrangian and Eulerian coordinates, i.e., A(X, t) and a(x, t)