Consider a system in R2 having only a finite number of equilibria. (a) Show that every limit set is either a closed orbit or the union of equilibrium points and solutions φt(X) such that limt→[infinity] φt(X) and limt→−[infinity] φt(X) are these equilibria. (b) Show by example (draw a picture) that the number of distinct solution curves in ω(X) may be infinite.

If you put a helium-filled balloon in the refrigerator, what will happen?

The junction rule describes the conservation of which quantity? note that this rule applies only to circuits that are in a steady state.

You are a researcher for a golf club manufacturer. you are given two identical looking cubes of a metal alloy. you are informed that they are made of the exact same material, but one is crystalline, whereas the other is amorphous. it is your job to determine which one is amorphous this one is more stress-resistant and is useful in reinforcing golf clubs. which of the following is the best way to determine which is which? a. determine the density of each cube. the more dense one is the amorphous solid. b. melt both cubes and look for a broader range of melting temperatures. the one that melts over a broader range of temperatures is the amorphous solid. c. determine the density of each cube. the less dense cube is the amorphous solid. d. melt both cubes and measure the range of melting temperatures. the one that melts over a narrower range of temperatures is the amorphous solid.