Consider the nonlinear system e the local stability properties of all equilibrium points when k-1 that the onigin becomes locally (c) consider the case with k 0 and u 0. show that the origin now is globaily and ut.0. (b) find a linear control law u ari +bz2 such asymptotically stable when kl. asymptotically stable. gt int use lyapunov funetlon

(a) assume the equation x = at^3 + bt describes the motion of a particular object, with x having the dimension of length and t having the dimension of time. determine the dimensions of the constants a and b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.) (b) determine the dimensions of the derivative dx/dt = 3at^2 + b. (use the following as necessary: l and t, where l is the unit of length and t is the unit of time.)

The heliocentric and the geocentric models of the solar system included these central principles

What is the thinnest soap film (excluding the case of zero thickness) that appears black when illuminated with light with a wavelength of 480 ? the index of refraction of the film is 1.34, and there is air on both sides of the film. express your answer in nanometers. hint 1. how to approach th