The two point charges, Q1 and Q2, are located at (1,2,0) and (2,0,0) respectively. Find the relation between Q1 and Q2 such that the total force on a test charge at the point P (-1,1,0) will have a) no x-component, b) no y-component.

Two charges attract each other with a force of 1.5 N. What will be the force if the distance between them is reduced to one-ninth of its original value?

Look through old and new magazines for examples of fads that have appeared since you were born. Create a collage illustrating those fads. Are some of them still around? Ask your parents or grandparents what some fads were when they were teenagers. Find pictures and make a poster to explain the fads.

In each of the following acid-base reactions, identify the Bronsted acid and base on the left and their conjugate partners on the right.\

$$\mathrm{N}_2 \mathrm{H}_4(\mathrm{aq})+\mathrm{HSO}_4{ }^{-}(\mathrm{aq}) \rightleftarrows \mathrm{N}_2 \mathrm{H}_5{ }^{+}(\mathrm{aq})+\mathrm{SO}_4{ }^{2-}(\mathrm{aq})$$

Find w in component form. u=i-k, v=51+2j; w=u-v

Solve the proportion. 10/y = 5/2

What is the net force (magnitude and direction) on charge $q_1$ exerted by the other two charges?

Use the Trapezoidal Rule and Simpson’s Rule to approximate the value of the definite integral for the indicated value of n. Compare these results with the exact value of the definite integral. Round your answers to four decimal places. $\int_{0}^{4} e^{-x / 2} d x, n=4$

Use the error formulas in Theorem 8.6 to estimate the errors in approximating the integral, with n = 4, using Simpson’s Rule.

$$\int_0^2\left(x^2+2 x\right) d x$$

Evaluate the given definite integrals. $\int_{0}^{1} \frac{1}{\sqrt{x}} d x$

Find exact values of the six trigonometric functions for each angle. Rationalize denominators when applicable. $-300^{\circ}$

A point charge q1 = 4.10 nC is placed at the origin, and a second point charge q2 = -2.90 nC is placed on the x-axis at x = + 20.0 cm. A third point charge q3 = 2.00 nC is to be placed on the x-axis between q1 and q2. (Take as zero the potential energy of the three charges when they are infinitely far apart.)

(a) What is the potential energy of the system of the three charges if q3 is placed at x = + 11.0 cm?

(b) Where should q3 be placed between q1 and q2 to make the potential energy of the system equal to zero?

On a separate sheet of paper, explain the following term by using it correctly in a sentence. Confucianism

Use the error formulas in Theorem 8.6 to estimate the errors in approximating the integral, with n = 4, using ( the Trapezoidal Rule

$$\int_0^1 e^{x^3} d x$$