Question

Suppose that f is an isometry for which there exists exactly one point P such that...

Suppose that f is an isometry for which there exists exactly one point P such that f(P)=P. Prove that f is a rotation. That is, prove that f is a direct isometry.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A nonidentity rotation has exactly one invariant point
A nonidentity rotation has exactly one invariant point
Let f : A → B and suppose that there exists a function g : B...
Let f : A → B and suppose that there exists a function g : B → A such that (g ◦ f)(a) = a and (f ◦ g)(b) = b. Prove that g = f −1 . Thank you!
Let a > 0 and f be continuous on [-a, a]. Suppose that f'(x) exists and...
Let a > 0 and f be continuous on [-a, a]. Suppose that f'(x) exists and f'(x)<= 1 for all x2 ㅌ (-a, a). If f(a) = a and f(-a) =-a. Show that f(0) = 0. Hint: Consider the two cases f(0) < 0 and f(0) > 0. Use mean value theorem to prove that these are impossible cases.
using these axioms ( finite affine plane ) : AA1 : there exists at least 4...
using these axioms ( finite affine plane ) : AA1 : there exists at least 4 distinct points , no there of which are collinear . AA2 : there exists at least one line with n (n>1) points on it . AA3 : Given two distinct points , there is exactly one line incident with both of them . AA4 : Given a line l and a point p not on l , there is exactly one line through p...
Suppose f is continuous for x is greater than or equal to 0, f'(x) exists for...
Suppose f is continuous for x is greater than or equal to 0, f'(x) exists for x greater than 0, f(0)=0, f' is monotonically increasing. For x greater than 0, put g(x) = f(x)/x and prove that g is monotonically increasing.
3. Let P(x) be a polynomial with P(0) > 0 and suppose that P has at...
3. Let P(x) be a polynomial with P(0) > 0 and suppose that P has at least one real zero which is not an integer multiple of π. Prove that there exists a solution to P(x) = sin2 x
Let f : [1, 2] → [1, 2] be a continuous function. Prove that there exists...
Let f : [1, 2] → [1, 2] be a continuous function. Prove that there exists a point c ∈ [1, 2] such that f(c) = c.
A function f : A → B is called constant if there exists b ∈ B...
A function f : A → B is called constant if there exists b ∈ B such that for all x ∈ A, f(x) = b. Let f : A → B, and suppose that A is nonempty. Prove that f is constant if and only if for all g : A → A, f ◦ g = f.
PROVE USING IVT. Suppose f is a differentiable function on [s,t] and suppose f'(s) > 0...
PROVE USING IVT. Suppose f is a differentiable function on [s,t] and suppose f'(s) > 0 > f'(t). Then there's a point p in (s,t) where f'(p)=0.
The continuous function has exactly one critical point. Find the x-values at which the global maximum...
The continuous function has exactly one critical point. Find the x-values at which the global maximum and the global minimum occur in the interval given. a) f'(1) = 0, f"(1) = -2 on 1 ≤ x ≤ 3 b) g'(-5) = 0, g"(-5) = 2 on -6 ≤ x ≤ -5
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT