If J is an n × 1 vector of ones and
1) Force F =(-8.00 N){+(6.00 N) j acts on a particle with position vector r = (3.00 m)i +(4.00 m)j. What are (a) the torque on the particle about the origin, in unit-vector notation, and (b) the angle between the directions of r and F?
Part A Vector A--3.00 i + 3.00 j and vector -3.00 + 4.00 j. What is vector C-A + Β? 0.00 i +7.00 j -3.00 + 7.00 7.00i +7.00 j 3.00 i-3.00 j 0.00 i + 3.00 j Submit Request Answer
(1 point) (a) Show that each of the vector fields F-4yi + 4x j, G-i ЗУ x2+y2 x?+yi J, and j are gradient vector fields on some domain (not necessarily the whole plane) x2+y2 by finding a potential function for each. For F, a potential function is f(x, y) - For G, a potential function is g(x, y) - For H, a potential function is h(x, y) (b) Find the line integrals of F, G, H around the curve C...
Hta11 2. Prove that for the (Hilbert) matrix is positive definite. i+j-1 i.j-1 Hnts: (Proceed from the definition to show that if a-(a a in n, then ar Ha>0 .a, is a nonzero vector a 1s a nonzero vector (ii)--= Í xi +j-2 ax (111) manipulate a' Ha into the integral of a positive function. i+ J Hta11 2. Prove that for the (Hilbert) matrix is positive definite. i+j-1 i.j-1 Hnts: (Proceed from the definition to show that if a-(a...
2. Let F be a field, n > 1 an integer and consider the F-vector space Mat,,n(F) of n × n matrices over F. Given a matrix A = (aij) E Matn,n(F) and i < n let 1 row,(Α-Σ@y and col,(A)-Žaji CO j-1 j-1 be the sum of entries in row i and column i, respectively. Define C, A EMat,,(F): row,(A)col,(A) for all 1 < i,j < n] C, { A E Matn.n(F) : row,(A) = 0 = col,(A) for...
5. Consider the language L = {1'0/1k e {0,1}* |i >01) >0 Ak = i*j}; to show that Lis! not a regular language using pumping lemma, the correct choice for the word is: a. 10011 x=1- b. 1POP 1P Z=1 Le 1290? 12p* Z=1P OPS 2P Y-101 YEK d. 10P1P y=1" t:P
3. Let I be the C-vector space with basis B = {1, cosx, sinx}. Define J: I + I by (Jf)(x) = 67 f(x +t) dt. Show that I is diagonalizable and find a basis of I consisting of eigenvectors of J.
(1 point) Enter vector answers in terms of i and j. To enter the 0 vector, you must type 0*i+0*j. For the curve r : R + R2 defined by r(t) = t(t – 2)i + t(t – 2)"; Find: a. r(0) = b. r'(0) = c. r() = d. r'() = e. r(1) = f.r' (1) = g. r(3) = h. r' (3) =
vector A = 4.5 i - 2.6 j + 1.4 k vector B = 2.5 i + 1.2 j - 1.7 k What is the vector A · B?
(4 points) On 01-01-15, J issued $9,000,000 of its 4%, 5-year term bonds dated 01-01-15. At the time the bonds were issued, similar bonds paid 4.125%. In conjunction with issuing the bonds, on 01-01-15, J incurred and paid $75,000 of issuance costs. The bonds pay interest every July 1 and January 1. J uses the effective-interest method to amortize any bond discount or premium. J prepares AJEs only as of every December 31. Prepare (and submit to me) a complete...