(Euler for systems) Solve $y_1^{\prime}=2 y_1-4 y_2, y_2^{\prime}=y_1-3 y_2, y_1(0)=3, y_2(0)=0$ by ($5$) ($10$ steps, $h=0.1$ ). Plot the solution in the $y_1 y_2$-plane.

Hydrogen $\left(\mathrm{H}_2\right)$ at $77^{\circ} \mathrm{F}, 1 \mathrm{~atm}$ enters an insulated reactor operating at steady state and burns completely with $x \%$ of theoretical air entering at $77^{\circ} \mathrm{F}$ , $1 \mathrm{~atm}$. Plot the adiabatic flame temperature for $x$ ranging from $100$ to $400 \%$.

Use separation of variables to find, if possible, product solutions for the given partial differential equation. $y \frac{\partial u}{\partial x}+x \frac{\partial u}{\partial y}=0$

Use the Chain Rule to find the indicated partial derivatives. $w=\sqrt{x^{2}+y^{2}} ; x=\ln (r s+t u)$, $y=\frac{t}{u} \cosh r s ; \frac{\partial w}{\partial t}, \frac{\partial w}{\partial r}, \frac{\partial w}{\partial u}$

Write a one-word description of each of the five terms in the incompressible Navier-Stokes equation $ho rac{\partial ec{V}}{\partial t}+ ho(ec{V} \cdot ec{ abla}) ec{V}= -ec{ abla} P+ ho ec{g}+\mu abla^{2} ec{V}$. When the creeping flow approximation is made, only two of the five terms remain. Which two terms remain, and why is this significant?

The link is pinned at $O$, and as a result of its rotation it drives the peg $P$ along the vertical guide. Calculate the magnitudes of the velocity and acceleration of $P$ if $\theta=c t \mathrm{rad}$, where $c$ is a constant.

Describe the cardiovascular counter-current mechanism in the human body.

The voltage follower has a
a. Closed-loop voltage gain of unity
b. Small open-loop voltage gain
c. Closed-loop bandwidth of zero
d. Large closed-loop output impedance

Fill in the missing parameter values for the BJT in the table if $r_{x}=250 \Omega$

Compare the work required at steady state to compress water vapor isentropically to $3\ \mathrm{MPa}$ from the saturated vapor state at $0.1\ \mathrm{MPa}$ to the work required to pump liquid water isentropically to $3\ \mathrm{MPa}$ from the saturated liquid state at $0.1\ \mathrm{MPa}$, each in $\mathrm{kJ}$ per $\mathrm{kg}$ of water flowing through the device. Kinetic and potential energy effects can be ignored.

What is cavitation? What causes it?

A transmitter delivers maximum power to an antenna when the antenna is adjusted to represent a load of $75-\Omega$ resistance in series with an inductance of $4 \mu \mathrm{H}$. If the transmitter operates at 4.12 MHz, find its internal impedance.

A certain solar-energy collector produces a maximum temperature of $100^{\circ} \mathrm{C}$. The energy is used in a cyclic heat engine that operates in a $10^{\circ} \mathrm{C}$ environment. WHat is the maximum thermal efficiency? What is it if the coolector is redesigned to focus the incoming light to produce a maximum temperature of $300^{\circ} \mathrm{C} ?$

What are superalloys? Why are they so named?