Show, by differentiating components, that (a)

d

dt

(A · B) =

dA

dt

· B + A ·

dB

dt
(b)

d

dt

(A × B) =

dA

dt

× B + A ×

dB

dt

,

just like the derivative of the product of two algebraic functions​

Aforklift raises a 1,020 n crate 3.50 m up to a shelf. how much work is done by the forklift on the crate? the forklift does j of work on the crate.

Refrigerant-134a flows through a carnot heat pump cycle at 0.5 kg/s. it is known that the maximum absolute temperature in the cycle is 1.1 times the minimum absolute temperature, and the net power input to the cycle is 2.5 kw. if the refrigerant changes from a saturated vapor to a saturated liquid during the heat rejection process, determine the maximum magnitude of the enthalpy of vaporization for this process in kj/kg (with 3 significant figures).

What is the name of the perceived change in a sound wave’s frequency due to motion between the observer and the sound source?