Question
Let t and s be transformations of the plane such that t(x, y) = (x+a, y+b)...
Let t and s be transformations of the plane such that t(x, y) =
(x+a, y+b) and s(x, y) = (x+c, y+d)
where a, b, c, and d are Real numbers. Let ?(?1, ?1) and ?(?2, ?2)
be any two points in the
plane. Show that (s ◦ t)(x, y) is an isometry.
Homework Answers
Answer #1
Not the answer you're looking for?
Similar Questions
1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and...
1. Let T(x, y, z) = (x + z, y − 2x, −z + 2y) and S(x, y, z) =
(2y − z, x − z, y + 3x). Use matrices to find the composition S ◦
T.
2. Find an equation of the tangent plane to the graph of x 2 − y
2 − 3z 2 = 5 at (6, 2, 3).
3. Find the critical points of f(x, y) = (x 2 + y 2 )e −y...
let r(t) = < x(t), y(t)>, a<t<b, be a smooth curve and F(x,y) = xi+yj, the...
let r(t) = < x(t), y(t)>, a<t<b, be a smooth curve
and F(x,y) = xi+yj, the work done by F on the curve equals
a) 1/2(x(b)^2+y(b)^2-x(a)^2-x(a)^2)
b) x(b)^2+y(b)^2-x(a)^2-x(a)^2
c) x(b)y(b)-x(a)y(a)
d)1/2(x(b)y(b)-x(a)y(a))
honestly, l don't remember clearly of the option. can you derive
from the question to give answers.
Let S be the boundary of the solid bounded by the paraboloid z=x^2+y^2 and the plane...
Let S be the boundary of the solid bounded by the paraboloid
z=x^2+y^2 and the plane z=16
S is the union of two surfaces. Let S1 be a portion of the plane
and S2 be a portion of the paraboloid so that S=S1∪S2
Evaluate the surface integral over S1
∬S1 z(x^2+y^2) dS=
Evaluate the surface integral over S2
∬S2 z(x^2+y^2) dS=
Therefore the surface integral over S is
∬S z(x^2+y^2) dS=
a) Let T be the plane 3x-y-2z=9. Find the shortest distance d from the point P0...
a) Let T be the plane 3x-y-2z=9. Find the shortest distance d
from the point P0 = (5, 2, 1) to T, and the point Q in T that is
closest to P0. Use the square root symbol where needed.
d=
Q= ( , , )
b) Find all values of X so that the triangle with vertices A =
(X, 4, 2), B = (3, 2, 0) and C = (2, 0 , -2) has area (5/2).
Let z(s,t) z(s,t) be a differentiable function of two variable s and t with continuous first...
Let z(s,t) z(s,t) be a differentiable function of two variable s
and t with continuous first partial derivatives. Assume further
that s=s(x,y), t=t(x,y) are differentiable functions of variables x
and y .
(a) find the general chain rule chain rule for (∂z/∂x)y . Your
subscripts will be marked.
(b) Let equations
F(x,y,s,t)=y+x^2+cos(t)−sin(s)+1=0,
G(x,y,s,t)=x+y^2−st−2=0,
implicitly define s , and t as functions of x and y .
Compute ∂s/∂x)y ∂t/∂x)y at the point P(x,y,s,t)=(1,−1,π,0).
(c) Let now z(s,t)=s^2+t. By using the...
Let r(t)=<x(t),y(t)>, from a<=t<=b, be a smooth curve and F(x,y)=xi+yj. What is the work done by...
Let r(t)=<x(t),y(t)>, from a<=t<=b, be a smooth
curve and F(x,y)=xi+yj. What is the work done by F on the curve
equal to?
a) 1/2(x^2(b)+y^2(b)-x^2(a)-y^2(a))
b) x(b)y(b)-x(a)y(a)
c) x^2(b)+y^2(b)-x^2(a)-y^2(a)
d)1/2(x(b)y(b)-x(a)y(a))
Let V be a finite dimensional vector space over R with an inner product 〈x, y〉...
Let V be a finite dimensional vector space over R with an inner
product 〈x, y〉 ∈ R for x, y ∈ V .
(a) (3points) Let λ∈R with λ>0. Show that
〈x,y〉′ = λ〈x,y〉, for x,y ∈ V,
(b) (2 points) Let T : V → V be a linear operator, such that
〈T(x),T(y)〉 = 〈x,y〉, for all x,y ∈ V.
Show that T is one-to-one.
(c) (2 points) Recall that the norm of a vector x ∈ V...
Let x = [1, 1]T , y = [1, 1]T ∈ R 2 and let f...
Let x = [1, 1]T , y = [1, 1]T ∈ R 2 and let f : R 2 =⇒ R 2 with
f(z) =z1.x + z2.y for any z = [z1, z2] T ∈ R 2 . Further, z = g(r)
= [r 2 , r3 ] where r ∈ R . Show how chain rule is applied here
giving major steps of the calculation, write down the expression
for ∂f ∂r , and also evaluate ∂f/ ∂r at...
Let (X; Y ) have a uniform distribution on the unit circle in the plane. (a)...
Let (X; Y ) have a uniform distribution on the unit circle in
the plane.
(a) Show that X and Y are not independent.
(b) Find P(X2 + Y 2 < 1=4) .
Let S be the set of all real circles, defined by (x-a)^2 + (y-b)^2=r^2. Define d(C1,C2)...
Let S be the set of all real circles, defined by (x-a)^2 +
(y-b)^2=r^2. Define d(C1,C2) =
√((a1 − a2)^2 + (b1 −
b2)^2 + (r1 − r2)^2 so that S is a
metric space.
Prove that metric space S is NOT a complete metric space. Give a
clear example.
Describe points of C\S as limits of the appropriate sequences of
circles, where C is the completion of S.
ADVERTISEMENT
Need Online Homework Help?
Get Answers For Free
Most questions answered within 1 hours.
ADVERTISEMENT
Active Questions
asked 31 minutes ago
asked 37 minutes ago
asked 58 minutes ago
asked 1 hour ago
asked 1 hour ago
asked 2 hours ago
asked 2 hours ago
asked 2 hours ago
asked 2 hours ago
asked 2 hours ago
asked 3 hours ago
asked 3 hours ago