[4] Given the following stress tensor in Cartesian coordinates: 1=274 -2.12 [Sym 4.07 3.69 -3.02 103 KPa 5.05 (a) Find the stress tensor in a new coordinate system rotated 30° around the z-axis. (b) Find the principal stresses and the direction of the σ11. [2] Let a=5i-6k; b=4i+2k Let r=5k. Express r as components parallel to a and b, i.e. find two scalars α and such that raa + Bb [3] (a) In a polar coordinate system, the position vector of a particle is given r = re,. Find an expression for the velocity and acceleration and reduce the derived expression to the case of circular motion with angular velocity co and angular acceleration a. (b) A rocket is fired vertically and tracked by a radar as shown in figure. When 0 = 60°, we have: = r = 9 km, = 21 m m/sec² I 8 0.02 rad/sec Find the velocity and acceleration vector of the rocket. V by X F [1] For the indicated range of indices (1 to 3 if not specified otherwise), write the expanded form of the indicial notation quantities given below: a) Aii, Bijj b) ai Tij, Tij aj c) Sii, Sij Sij, Sij Sjk d) Sij Sjk Ski, Sij Ajk e) + pb, = 0 Ox; f) o₁ = D, E, i,j = 1,2,...,6 P