Prove that the contracted product of two tensors a. b, with components aikbk; is a tensor of order two. b. show that the doubly contracted product aįjbij of a symmetric tensor a and an antisymmetric tensor b vanishes c. show that a symmetric tensor remains symmetric under any transformation of axes d. given a tensor a and a vector b, prove that the contracted products a b and b · a are both vectors, that is show that aijb; and bịajj are components of vectors. note that they are not the same vector unless a is symmetric.

Aracecar driver has to hold on tightly when going around a banked curve. approximately what is the centripetal force on a 2220.0 kg car going around a circle with a diameter of 190.0 meters at 25.0 m/s?

Adiver named jacques observes a bubble of air rising from the bottom of a lake (where the absolute pressure is 3.50 atm) to the surface (where the pressure is 1.00 atm). the temperature at the bottom is 4.00 ∘c, and the temperature at the surface is 23.0 ∘c. what is the ratio of the volume of the bubble as it reaches the surface (vs) to its volume at the bottom (vb)? if jaques were to hold his breath the air in his lungs would be kept at a constant temperature. would it be safe for jacques to hold his breath while ascending from the bottom of the lake to the surface?

Against his financial advisor's advice, frank has decided to invest his money in some risky stocks because he once made quite a bit of money in the stock market. his decision illustrates a. the representativeness heuristic b. overconfidence c. the availability heuristic d. confirmation bias select the best answer from the choices provided