Show that if all components of any tensor of any rank vanish in one particular coordinate system they vanish in all coordinate system

Suppose that a mass of 2 kg is attached a spring whose spring constant is 50. the system is damped such that b = 12 . the mass is set in motion with an initial velocity of -8 m/s at a position 0 meters from equilibrium. set up and solve a differential equation that models this motion. write your solution in the form a cos ( ω t − α ) where α is a positive number. use your solution to fill in the information below: what is the amplitude of the motion? what is the value of ω ? what is the phase shift?

The velocity of a car traveling in a straight line increases from 0 meters/second to 30meters/second in 8 seconds. what is the average acceleration of the car?

Using a caesar cypher with an offset of three characters (a -> d, b -> e, z -> c), what would be the correct cypher text for the plain text "attack at dawn"?