How did geographic factors help Great Britain to control territory around the world?

Discuss the validity of each statement. Venn diagrams may be helpful. If the statement is true, explain why. If $A \subset B$, then $B^{\prime} \subset A^{\prime}$.

A 200 MHz, left-hand circularly polarized plane wave with an electric field modulus of 5 V/m is normally incident in air upon a dielectric medium with $\epsilon_{\mathrm{r}}=4$ and occupies the region defined by $z \geq 0$. (a) Write an expression for the electric field phasor of the incident wave, given that the field is a positive maximum at z=0 and t=0. (b) Calculate the reflection and transmission coefficients. (c) Write expressions for the electric field phasors of the reflected wave, the transmitted wave, and the total field in the region $z \leq 0$. (d) Determine the percentages of the incident average power reflected by the boundary and transmitted into the second medium.

Let $a \rightarrow \infty$ in Exercise 9 and prove that

$$\int_{\mathbf{R}^{2}} f(x, y) d x d y=\int_{0}^{\infty} \int_{0}^{2 n} f(T(r, \theta)) r d r d \theta$$

for continuous functions $f$ that decrease sufficiently rapidly as $|x|+|y| \rightarrow \infty$ (Find a more precise formulation.)

If the product of the first three prime numbers is divided by the sum of the first three prime numbers, what is the quotient?

Use the standard forms of valid arguments to draw a valid conclusion from the given premises. The writers of My Mother the Car were told by the network to improve their scripts or be dropped from prime time. The writers of My Mother the Car did not improve their scripts. Therefore, ...

Write a system of equations having $\{(-2,7)\}$ as a solution set. (More than one system is possible.)

At time t =0 hours a car starts from Port Wakefield, a distance of 95 km from Adelaide, and travels with speed given by $v(t)=50+50 e^{-t} \mathrm{km} \mathrm{h}^{-1}$ towards Adelaide. a. Sketch a graph of the speed of the car for $0 \leqslant t \leqslant 1.$ b. What are the maximum and minimum speeds of the car for $0 \leqslant t \leqslant 1 ?$ c. Show that the distance d of the car from Adelaide after one hour is less than 27 km. d. By dividing the time of travel into 2 half hour intervals, estimate the distance of the car from Adelaide after 1 hour of travel. e. Improve the estimate you made in d by considering 4 time intervals of a quarter of an hour each.

Explain how you see and track the pathway of light from the cornea to the occipital lobe of the brain.

Consider the intimation you have learned about social stratification and social class, social classes in the United States and types of social mobility. Then design a chart, diagram, or other visual to explain how each of these helps you understand the others.

A bird bath is filled with water. Over time, the water evaporates as shown in the table below:

$$\begin{matrix} \text{Time t (hours)} & \text{3} & \text{6} & \text{9} & \text{12} & \text{15} & \text{18} & \text{21} & \text{24}\\ \text{Water remaining V (litres)} & \text{6.7} & \text{3.6} & \text{2} & \text{1.1} & \text{0.6} & \text{0.32} & \text{0.18} & \text{0.10}\\\end{matrix}$$

Estimate the amount of water which has evaporated after 10 hours.

Let D be the region bounded by $y=x^{2}, y=x+2$, and y=-x. a. Show that $\int_{D} x d A=\int_{0}^{1} \int_{-y}^{\sqrt{y}} x d x d y+\int_{1}^{2} \int_{y-2}^{\sqrt{y}} x d x d y$ by dividing the region D into two regions of Type II, where $D=\{(x, y) | y \geq x^{2}, y \geq-x, y \leq x+2\}$. b. Evaluate the integral $\iint_{D} x d A$.

A jet plane has a takeoff speed of $v _ { \text { to } } = 75 \textrm{m/s}$ and can move along the runway at an average acceleration of $1.3 m/s^2$. If the length of the runway is $2.5 \textrm{km}$, will the plane be able to use this runway safely? Defend your answer.

Answer yes or no and explain why or why not. If $8 n=180,$ does $8 n \div 8=180 \div 8 ?$