What causes the phenomenon of "red shift" and "blue shift" in astronomy? * constructive interference
doppler effect
different wavelengths of light
destructive interference

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k

Consider a small frictionless puck perched at the top of a fixed sphere of radius r. if the puck is given a tiny nudge so that it begins to slide down, through what vertical height will it descend before it leaves the surface of the sphere? [hint: use conservation of energy to find the puck's speed as a func e conservation of energy to find the puck's speed as a function of its height at what value of this normal force does the puck leave the sphere? ] here on the puck.

Water flows through a garden hose which is attached to a nozzle. the water flows through hose with a speed of 2.19 m/s and through the nozzle with a speed of 19.8 m/s. calculate the maximum height (in m) to which water could be squirted if it emerges from the nozzle and emerges with the nozzle removed.