$1\mathrm{.}2$ Identify the four elements of control: measurement, error detection, compensation, and feedback for the following control systems:

a$.$ A common bome refrigerator

b$.$ A home air conditioner

c$.$ The steering of an automobile

d$.$ An automobile's cruise control

$1\mathrm{.}11$ Determine if the following equations are linear or nonlinear:

a$.y=4-15x$

b$.y=3x-\frac{3}{x}$

c$.y=sin(2x+4)$

d$.y=2x+4\frac{d^{2}x}{d{r}^2}$

e$.\frac{dy}{dt}+4y=\frac{dx}{dt}+7{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xdt$