Example 2.8.3 Let G = SO(2), the group of all 2 x 2 real matrices which are orthogonal, that is, they satisfy the relation AA' = I, and which have determinant 1. The set G is in one-to-one correspondence with the unit circle in R2 by the map %3D :). X2 (x1, 22) – ( -x2

Q: The differential equation y" + 4y + 4y 0 has two solutions yı = e2x and y2 = Which of the followings…

A:

Q: rect answ

A: Introduction: According to the chance formula, the chance of an incident occurring is adequate to…

Q: Evaluate lim, o[cos()].

A:

Q: F{xe 12l} = a) -8iX (16+X²)? b) -16i) (16+X²)? c) 16iX (16+A?)? d) 8iX (16+X*) e) None of these

A: We compute Fourier transform of xe-4|x|.

Q: 9.1 A General Social Survey asked: "Do you support or oppose the following measures to deal with…

A: (a) Given the Fit loglinear modes (GH,GI), (GH,HI), (GI,GI) and (GH,GI,HI) we will show that models…

Q: s expansion of 2 , valid in the re of 1/z2 is:

A:

Q: Select the correct answer. Which limit does not exist? OA lim i 2 - 1 I + 1 О В. lim 12 – 9 - 2 Oc…

A:

Q: Find the volume of the solid that results when the region enclosed by y = e", y = 0, x = 0, x = ln…

A:

Q: Find the area under the curve f(1) = r' o I = [– 0.5, 4.5] using the M %3D

A: Introduction: The formula for the mid-point rule for a continuous function f(x) on a,b is given by,…

Q: Mel is teaching Travis how to use a compass and a straightedge to construct a square inscribed in a…

A:

Q: Show that the equation dy + 2k possesses solutions of the form 00 -kt E C, e cos (C, x+ E,) cos…

A:

Q: Draw the graphs and find the between the area curves f (x) = (-1)**'x² + (-1)**' (b+3)x+(-1)°(c+5)…

A: This problem is an application of Definite Integrals and I find the area enclosed between the curves…

Q: Drag each tile to the correct box. Arrange the hyperbolas in increasing order of the horizontal…

A: To arrange the given hyperbolas in increasing order of the horizontal width of their asymptote…

Q: 5. Find a general solution of the differential equation: y" + 4y' = 2x – 1

A:

Q: 2. Determine if the series is absolutely convergent, conditionally convergent, or divergent. cos(nT)…

A:

Q: Let W1 be the set: Determine if Wi is a basis for R' and check the correct answer(s) below. A. W1 is…

A: Here W1 be the set given by W1=100, 110, 111. We have to determined the given set W1 is a basis for…

Q: dx dy 2 x ex y2 + xy+y

A:

Q: 5n 9. Use the L'Hopital's rule to determine if the sequence an = () converges or diverges as limit n…

A:

Q: い) Ev 3. 0一 234 い

A: given  fx=x2-x+sinx-1 f'x=2x+cosx-1 xn+1=xn-fxnf'xn εr=xn+1-xnxn+1

Q: (6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6) How many possible outcomes are there? Let E = the ways in…

A:

Q: ral of the d D- 1)y is

A:

Q: Use the present value formula to determine the amount to be invested now, or the present value…

A: Given that, The desired accumulated amount =$85,000 compound semiannually interest rate=8% Number of…

Q: Fー1 e-5id 1+(A+6)² S a) ebi(z-5)-|r-5| O b) None of these Oc). -6i(x+5)-|x+5| d) Je6i(2+5)-|z+히 O e)…

A:

Q: The number of automobiles in a certain small town was in 1890, and in 2015 and 2420 in 2020. If we…

A: Graphically, the linear function representing the relationship between an independent variable let's…

Q: (D3 - 3D - 2)y =0; when x =0, y=0, y' = 9, y" = 0. 2x y = (-2 + 3r)e¯*+2e² B В y = (-1+ 2x)e2* + 2e…

A:

Q: a - b 1.2 -0.8 Find an invertible matrix P and a matrix C of the form such that A = has the form A =…

A:

Q: Question 8 (. Use triple integral in spherical coordinates to find the volume of the solid bounded…

A:

Q: Question 5 [1 k] 2 1 Let A = a) Find the eigenvalues of A in terms of k, in simplified surd form. b)…

A:

Q: Find the time it would take for the general level of prices in the economy to double at an average…

A:

Q: How many sequences of n coin flips, wheren> 1/ contain no pair of consecutive heads (no HH) and no…

A: Solution

Q: Let -13 -11 B = -30 -25 -20 -15 -9 -7 (a) Find the reduced row echelon form of the matrix B. rref(B)…

A:

Q: Find a general solution of the differential equation: y"" - 4y" – 3y' + 18y = 3e*

A:

Q: Suppose that E is a measurable set of finite measure and that (fn) is a sequence of measurable…

A:

Q: DEMAND LOW HIGH Alternative 1 $10,000 $ 5,000 -$ 2,000 $30,000 Alternative 2 $40,000 Alternative 3…

A: I solved all three questions as one part.

Q: x² y" - 3xy + 3y = 0. (a) Verify that y = cx + c2x is the general solution of the differential…

A:

Q: nose Laplace (28+4) at t

A:

Q: ag the tiles to the boxes to form correct pairs. Not all tiles will be used. atch the resulting…

A:

Q: Let -1 -4 B = 2 7 2 -2 9. (a) Find the reduced row echelon form of the matrix B. ref(B) = (b) How…

A:

Q: : For a 4 x 4 linear system AX = O if (3, 0,0,0) is a solution for this system, Then

A:

Q: -5i시 F-1! e 1+(A+6)? O a) L e6i(x+5)-|æ+5| O b) e6i (x-5)-2-5| O c) None of these d)…

A:

Q: SHOW THE SOLUTIO N: Solve using J Mdx(y = constant) +J Nthe term not contained x)dy = A (3x² – 2xy +…

A:

Q: Time height 1stdifference 2nd difference 0.0 320 1.0 315 2.0 300 3.0 275 4.0 240 a) Find the finite…

A: Suppose x is the independent variable and y is the dependent variable. The rate of change is…

Q: tutt. 0 0, which satisfies the boundary conditions u(0, t) = u(3, t) = 0 and the initial The…

A:

Q: Drag each tile to the correct box. The Big Bills are a charitable organization that conducts seven…

A:

Q: Let R = {(x, y) E R² | In y <x <1n1< y<e} and let S be the surface defined by the vector function…

A: As per the question we are given a surface S defined by the vector function R(u,v) And we have to…

Q: Express the radical using the imaginary unit, i. Express your answer in simplified form. ±V-44 = +

A: We know that , complex number can be written in the form , a + bi . Here , a = Real part of complex…

Q: 4. If 0< f'(x)< for all x e R, show that f(-1) < f (1)<10+ f(-1).

A: Here we have to use property of increasing function . and Mean value theorem (MVT) Suppose f(x) is a…

Q: x, 0<x < 1 3, 1< r < 2 S Let f(x) = 39, the Fourier sine series of f . At x = 0, 2] converges to on…

A: