Show the dot product of two vectors are invariant

Assume that a person skiing high in the mountains at an altitude of h = 15100 ft takes in the same volume of air with each breath as she does while walking at sea level. determine the ratio of the mass of oxygen inhaled for each breath at this high altitude compared to that at sea level. assume that the air composition (i.e. % of air that is oxygen) is the same at sea level as it is at 15100 ft.

Two carts, one of mass 2m and one of mass m, approach each other with the same speed, v. when the carts collide, they hook together. assume that positive momentum is to the right. which graph best represents the momentum of both carts over time, before and after the collision?

An alarm clock has a current of 4.5 amps and a resistance of 3.2 ohms. what is the voltage in the circuit? a.1.4 volts b.0.71 volts c.14 volts d.46 volts