P = Power, V = Voltage, I = Current, and R = Resistance. Which of the following relations is incorrect?

Choices:

V = I R

P = V R

P = VI

I = V/R

Given two sets S and T, the direct product of S and T is the set of ordered pairs S × T = {(s, t)|s ∈ S, t ∈ T}.Let V, W be two vector spaces over F.

(a) Prove that V × W is a vector space over F under componentwise addition and scalar multiplication (i.e. if (v1, w1),(v2, w2) ∈ V × W, then (v1, w1) + (v2, w2) = (v1+w1, v2+w2) and a(v, w) = (av, aw) for any (v, w) ∈ V ×W, a ∈ F).

(b) If dim V = n and dim W = m, prove that dim V × W = n + m by constructing a basis.

1.) Translate the following C code to MIPS assembly code. Assume that the variables f, g, h, i, and j are assigned to registers $s0, $s1, $s2, $s3, and $s4, respectively. Assume that the base address of the arrays A and B are in registers $s6 and $s7, respectively

  B[8] = A[i-j];

2.Translate the following C code to MIPS assembly code. Assume that the values of v in $a0, k in $a1, temp in $t0.

// leaf procedure that swaps v[k] and v[k+1]

void swap(int v[], int k)

{
int temp;
temp = v[k];
v[k] = v[k+1];
v[k+1] = temp;
}

1) Of four properties that define the conditions of gas (pressure, Volume, temperature and moles), which two are studied in the Boyle's Law experiment? explain briefly how the remaining two are unchanged during the experiment.

2) Which two are studied in Part B of this experiment? Explain briefly how the remaining two are unchanged during the experiment.

3) when a flask of gas is cooled, the pressure of the gas will change. what would happen to the gas if it were cooled to an extremely low temperature?

2
Let u,v, and w be vectors, where u=(1,2,3,-1), v=(2,3,1,5) and w=(3,5,4,4).

2.1
Construct a basis for the vector space spanned by u, v and w.

2.2
Show that c=(1,3,2,1) is not in the vector space spanned by the above vectors u,v and w.

2.3
Show that d=(4,9,17,-11) is in the vector space spanned by the above vectors u,v and w, by expressing d as a linear combination of u,v and w.

Find an article relating to Time Value of Money or Asset Valuation techniques from any medium, briefly summarize the article, explain how you found the article particularly useful or timely, and give your personal reactions to the article. Be sure to provide the title of the article, the author(s), and the reference for the article.

Find an article relating to Time Value of Money or Asset Valuation techniques from any medium, briefly summarize the article, explain how you found the article particularly useful or timely, and give your personal reactions to the article. Be sure to provide the title of the article, the author(s), and the reference for the article.