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.

Laboratory experiments, observational field studies, and model-building are all examples of different forms of scientific investigations.  in what way do laboratory experiments primarily differ from other forms of scientific investigations?   a.  a laboratory experiment is the only accepted form of investigation within the scientific community.  b.  studies about how things behave in nature or studies involving very large objects are best answered through laboratory experiments.  c.  laboratory experiments involve the identification and control of variables.  d.  data can only be generated through laboratory experiments, not other forms of investigation.

An object moves from the position +34m to the position -15m in 15 seconds. what is it's total displacement? what is it's average velocity?

John throws .4 kg ball with velocity of 18 m/s. hits .2 kg bottle and bottle flies 25 m/s. how fast is ball traveling after hitting the bottle?