Please help me with these three questions. Thank you.

8. The velocity of a satellite is '01 east, '02 north, '03 up as measured from a cartesian basis located at longitude up, latitude A. What are the corresponding velocity components with respect to the Earth basis? 9. The velocity of a satellite is '01 east, '02 north, '03 up as measured from a cartesian basis located at longitude cpl, latitude A1. What are the corresponding velocity components with respect to a local basis at longitude (pg, latitude A2? Derive and explain an algorithm to compute those components. 10. In relation to 4147), prove that if v,- = aijvj for all '0,- then adj = 6,5. Orthonormality. There are 9 direction cosines cos ij (in 3D space) but orthonor- mality of both bases imply several constraints, so these 9 angles are not independent and the Q matrices have very special characteristics. These constraints follow from (137), (138) which must hold for any (v1, V2, V3) and (v1, V2, Vg). Substituting (138) into (137) yields vi = qikqjk v;, Vv; + qikqjk = dij (147)