Consider a rotation T (x) = Ax- in R3. (That is, A is an orthogonal 3 × 3 matrix with determinant 1.) Show that T has a nonzero fixed point [i. e., a vector v- with T (v) -= v]. This result is known as Euler’s theorem, after the great Swiss mathematician Leonhard Euler (1707–1783). Hint: Consider the characteristic polyno- mial fA(λ). Pay attention to the intercepts with both axes. Use Theorem 7.1.4.

total = principal × ( 1 + rate ) ^ years

total = 600 * (1.04)^5

total = 729.99

answer is c

step-by-step explanation:

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source

246

step-by-step explanation: