Because T is a second-order Cartesian tensor, its components t; in the primed system are expressed in terms of the unprimed components by Eq 2.65 as tij = aiqtqmajm or T' = ATAT (3.33) The matrix formulation of Eq 3.33 is very convenient for computing the primed compo- nents of stress as demonstrated by the two following examples. Problem 3.12 The stress matrix referred to axes Px1x2x3 is given in ksi by 14 0 21 [tij] = 0 21 0 21 0 7 Let rotated axes Pxx2x3 be defined with respect to axes Px1x2x3 by the table of base vectors e2 3 e2/7 3/7 6/7 2 3/7 -6/7 2/7 e 6/7 2/7 -3/7 (a) Determine the stress vectors on planes at P perpendicular to the primed axes; determine t(), t(), and t() in terms of base vectors 1, 2, and 3. (b) Project each of the stress vectors obtained in (a) onto the primed axes to deter- mine the nine components of [t]. (c) Verify the result obtained in (b) by a direct application of Eq 3.33 of the text.