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.

hi! i think the answer is 1/2 : )

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²