Consider the linear transformation T: R^4 to R^3 defined by T(x, y, z, w) = (x +2y +z, 2x +2y +3z +w, x +4y +2w)

a) Find the dimension and basis for Im T (the image of T)

b) Find the dimension and basis for Ker ( the Kernel of T)

c) Does the vector v= (2,3,5) belong to Im T? Justify the answer.

d) Does the vector v= (12,-3,-6,0) belong to Ker? Justify the answer.

Consider four 60·nC charges placed at the corners of a square, which is 3.6·m on a side. The charges on the bottom are both positive, and the charges on the top are both negative.

(a) Find the electric field at the center of the square, in units of V/m. vector E = 0 i hat + 235.7 j

(b)Find the electric field at the midpoint of the right side, in units of V/m. vector E = _ i hat + _ j

Please help find the answer to part B.

A. Show that the ideal gases following PV=nRT satisfy (dp/dv)(dv/dt)(dt/dp)=-1.

B. Show that van see waals fluids following P=(RT/V-b) - a/V^2 satisfy (dp/dv)(dv/dt)(dt/dp)=-1.

C. Use the fundamental relation, dH=TdS + VdP and Maxwell equations to show that (dH^ig/dV) = 0, which means that enthrall of ideal gases us independent of volume.

1) You have three vectors with (∣v⃗∣,θ)(∣v∣,θ) pairs of (11,75∘)(11,75∘), (8,50∘)(8,50∘), and (10,−100∘)(10,−100∘).

If you wanted to add a fourth vector to those first three such that the sum of all four vectors were 0, what would that fourth vector be? Give your answer as a (vx,vy)(vx​,vy​) pair. Give your answer to 1 decimal point. Then show it as a (∣v⃗∣,θ)(∣v∣,θ) pair.

Dameeba Corp has a current D/V-ratio of 10% with expected cost of debt 2,1% p.a. The levered equity beta is 0,75. An increase to a target D/V-ratio of 90% is now planned increasing the expected cost of debt to 4,3% p.a. The corporate tax rate is 20%. The risk-free rate is 1% and the market risk premium 5% p.a. What will be Dameeba Corp’s new equity beta?

a. 0,885 b. 1,142 c. 1,030 d. 1,208

Alfaeba Corp has a current D/V-ratio of 85% with expected cost of debt 5,7% p.a. The levered equity beta is 2,5. A reduction to a target D/V-ratio of 50% is now planned lowering the expected cost of debt to 4% p.a. The corporate tax rate is 20%. The risk-free rate is 1% and the market risk premium 5% p.a. What will be Alfaeba Corp’s new WACC?

a. 5,901% b. 6,47% c. 6,021% d. 6,87%

S_3 is the vector space of polynomials degree <= 3. V is a subspace of poly's s(t) so that s(0) = s(1) = 0. The inner product for two poly. s(t) and f(t) is def.: (s,f) = ([integral from 0 to 1] s(t)f(t)dt). I would like guidance finding (1) an orthogonal basis for V and (2) the projection for s(t) = 1 - t + 2t^2. Thank you!

Design a three part, 1D, Kinematics problem, Solve it (finding the total time and distance traveled) and show it x(t), v(t), a(t) graph.

make the initial x(t) as zero but the initial v(t) can not be zero. for example, you could start at a constant speed, then slow to a stop, then speed up in the same direction (or go in reverse). Or you could start at certain speed, immediately speed up, then stay at that new speed for (say 200 meters) a while

Be sure to answer all parts. In acidic solution, O3 and Mn2+ ions react spontaneously: O3(g) + Mn2+(aq) + H2O(l) → O2(g) + MnO2(s) + 2H+(aq) E o cell = 0.84 V

Write the balanced half-reactions and calculate E o manganese when given E o ozone = 2.07 V.

Include states of matter in your answers.

Reduction half-reaction:

Oxidation half-reaction:

E o manganese=

You watched the documentary "Illicit: The Dark Trade". What in the documentary do you think was most interesting about globalization and crime? Why? Also, what would you have liked to see and learn in the documentary, but it was not there? In other words, what do you think was missing in the documentary that would have made us understand globalization of crime better if it were covered in the documentary?

Video links:

https://www.youtube.com/watch?v=l2Sg5lxVzlo&t=6s

https://www.youtube.com/watch?v=OX43xLU8Ip8