Three protons are initially very far apart. Calculate the work that must be done in order to bring these protons to the vertices of an equilateral triangle of side

$$5.0 \times 10 ^ { - 16 } \mathrm { m }$$

.

Two long parallel plates are separated by a distance of 15.0 cm. The bottom plate is kept at a potential of −250 V and the top at

$$+ 250 \mathrm { V }$$

. A charge of

$$- 2.00 \mu \mathrm { C }$$

is placed at a point 3.00 cm from the bottom plate. a. Find the electric potential energy of the charge. The charge is then moved vertically up to a point 3.00 cm from the top plate. b. What is the electrical potential energy of the charge now? c. How much work was done on the charge?

Distinguish between the living and nonliving components in ecosystems and give two examples of each. What are two other terms used to describe these ecosystem components?

How did contact between the European arrivals and the native peoples of the Americas affect both groups?

Four protons, each with mass M and charge +e, are initially held at the corners of a square that is d on a side. They are then released from rest. What is the speed of each proton when the protons are very far apart?

Fill in the blank. Since

$$y ^ { 2 } + 2 y + 1 = ( y + 1 ) ^ { 2 }$$

, we call

$$y ^ { 2 } + 2 y + 1$$

a _____-square trinomial.

Solve each of the differential equations. Several can be solved by at least two different methods.

$$e^{2 x} y^{2} d x+\left(e^{2 x} y-2 y\right) d y=0$$

A charge q of 10.0 C is placed somewhere in space. What is the work required to bring a charge of 1.0 mC from a point X, 10.0 m from q, to a point Y, 2.0 m from q? Does the answer depend on which path the charge follows?

Explain what you think Joseph Campbell means by an "Ariadne thread." Have you had an Ariadne thread in your life? What was it?

On Sunday, 17-year-old Rosa Martinez completed her first marathon. Her time of 2 hours and 45 minutes won't break any records, but she's proud to have finished the race—in her wheelchair. "I lost the use of my legs in a car crash three years ago," says Rosa. "I was really depressed, but getting into wheelchair sports inspired me. I started focusing more on what I could do in my chair than on what I couldn't do." To train for the marathon, Rosa says she did "a lot of aerobic exercises to strengthen my heart and lungs, and a lot of work on my upper body strength." While she's proud of her achievement Rosa isn't going to rest on her laurels. She's already looking ahead to next year's marathon, and she's determined to beat her time from this year. Describe the physical and mental qualities that make Rosa a successful athlete. How might she apply these qualities to other aspects of her life?

Library A has 10,000 novels, 5000 biographies, and 5000 children's books. Library B has 15,000 novels, 10,000 biographies, and 2500 children's books. Library C has 4000 novels, 700 biographies, and 800 children's books. Find A + B. Does the matrix have meaning in this situation? Explain.

A spacecraft of mass 30 000 kg leaves the Earth on its way to the Moon and lands on the Moon. Plot the spacecraft’s potential energy as a function of its distance from the Earth’s centre. (The Earth-Moon distance is

$$3.8 \times 10 ^ { 8 } \mathrm { m }$$

. Take the mass of the Earth to be

$$5.97 \times 10 ^ { 24 } \mathrm { kg }$$

and the mass of the Moon to be

$$7.35 \times 10 ^ { 22 } \mathrm { kg }$$

.)

Use words to write the number 90,807,060

Two conducting spheres are separated by a distance that is large compared with their radii. The first sphere has a radius of 10.0 cm and has a charge of

$$2.00 \mu \mathrm { C }$$

on its surface. The second sphere has a radius of 15.0 cm and is neutral. The spheres are then connected by a long conducting wire. a. Find the charge on each sphere. b. Calculate the charge density on each sphere (charge density is the total charge on the sphere divided by the surface area of the sphere). c. Calculate the electric field on the surface of each sphere. d. Comment on your result in the light of your answer to part b. Why is it stated that the wire is long?