Linear elasticity homework ob2 In r 2 b cos 20 r2 2b2 2 4 Find the...
Consider the linear transformation T: R4 + R2 defined as T(11,12,13,14)=(-221 +22 +2 14,322 -14) Find the standard matrix for T: ab sin(a) f 8 a 12 . ar What is the dimension of ker(T)? Number Is T one-to-one? Enter one yes no Write the standard matrix for HoT, where H is the reflection of R2 about the line y=1. ab sin(a) f αο α Ω TI д
Find the area inside the lemniscate r2 = 18 cos 20 and outside the circle r= 19. The area inside the lemniscate and outside the circle is (Type an exact answer, using a as needed.)
Could you please 1.question ЕЕ211 Electromagnetic Field Theory 1 Homework 2 Due by 12th of Nov, 2018 at 5 PM ANTALYA BILIM UNIVERSITY Homework 2 Q1. Given three vectors A, B, and C A-a +2a, -3a, Find (a) unit vector along A. (b) IA -BI (c) A.B (d) the angle between vectors A and B (e) The vector component of A in the direction of C. (f) AxC (g) A. (x C) and (A x B).C (h) (A x B)...
You are given the metric of a 4-dimensional Einstein universe in terms of spherical polar coordinates r, 0, ø, -dt2e20(1) dr2 +r2 (d02 + sin2 0dp2), ds2 (a) Use the variational principle 2 ds dA 0, dA to find the geodesic equation for r with parameter A, between given points X1 and A2. (b) Deduce or otherwise show that Г — Ф", Ге — —re 20, To= -rsin2 Oe-24 rr =0 if uv and T T You are given the...
Problem 1) Consider a f r-o 05m with permeability -Kh" 100H1m shown in Figure laAantrof 1+cos) A is injected to coil 1 with N,10 turns a) [5 marks] Draw the equivalent magnetic circuit and determine the values for the magnetomotive force and the reluctances b)(3 marks! Calculate the magnetic fluxes ф..ф, in each section ofthe core. ) [5 marks] Now place coils 2 and 3 with N,-5 and N,-15 turns around the core as shown in figure 1.b. Find current...
11. Suppose S: R R2 is the linear transformation with matrix -3 11 [2 -6 2 relative to the bases & and &. Find the matrix of S with respect to the bases (1,0, 1), (1,0,0), (1, 1,0)) and ((1,-1). (2,0). 11. Suppose S: R R2 is the linear transformation with matrix -3 11 [2 -6 2 relative to the bases & and &. Find the matrix of S with respect to the bases (1,0, 1), (1,0,0), (1, 1,0)) and...
2) Let B = {(1, 3, 4), (2,-5,2), (-4,2-6)) and B/-(( 1, 2,-2), (4, 1,-4), (-2, 5, 8)) be 5 ordered bases of R2. Let x = | 8 | in the standard basis of R2. a) Use a matrix and x to find L18 ]B. b) Use a matrix and [X]B to find [x)B/. c) Use a matrix and [X]B/ to find x in the standard basis of R2, d) Draw a diagram of the steps a), b), and...
-00)0) 2 (AB 22) Let L : R, R2 be a linear transformation. You are given that L 2- 3 (a) Find the matrix A that represents L with respect to the basisu-| | 2-1 1-1 4 1 and the 6 standard basis F1 (b) Find the matrix B that represents IL with respect to the standard basis in both R3 and R2
2. (20 pts.). In the cireuit showa in the diagram, find the resistance R, current through it and the unknown emf €2. I lere r-30 V, ea-100 V, R2·5f1, R, R_ 4 Ω, R = 1 n, the current through R2 reads 12 = 5 A and the current through Rs is 1s5 A corresspondly
QUESTION 4 Given the equation of a point, r(t) ( I)i ( -I)j Sketch the graph of r(r) = (1 + l)i + (r2-Dj fr-2 2. Draw the (a) t 4 marks) position vector r(0) on the same diagram. b) Find the unit tangent vector of the point at 0 and show it on the same diagram in (a). Explain what you understand about the direction of the tangent (5 marks)