The characteristic polynomial is det(A - λI) = det([[1-λ, 2], [3, 4-λ]]) = (1-λ)(4-λ) - 6 = λ^2 - 5λ + 2.

The characteristic polynomial is given by det(A - λI) = det([[2-λ, 1], [1, 2-λ]]) = (2-λ)(2-λ) - 1 = λ^2 - 3λ + 3.

For a right triangle, the circumradius R = hypotenuse/2 = 13/2 = 6.5.

Circumradius R = (abc)/(4K), where K is the area. Area K = 24 (using Heron's formula). R = (6*8*10)/(4*24) = 5.

The circumradius R of a triangle can be calculated using the formula R = (abc)/(4 * Area). Here, Area = 84 cm², so R = (7 * 24 * 25)/(4 * 84) = 13.

The circumradius R of an equilateral triangle is given by R = a/(√3).

R = (abc) / (4 * Area). Area = 84, R = (7 * 24 * 25) / (4 * 84) = 12.

The circumradius R of a triangle is given by the formula R = abc/(4A), where A is the area of the triangle.

The coefficient of static friction (μs) is given by μs = F/N, where F is the force and N is the normal force. Here, μs = 20 N / 50 N = 0.4.

Coefficient of variation = (Standard deviation / Mean) * 100 = (10 / 50) * 100 = 20%.

Coefficient of Variation = (Standard Deviation / Mean) * 100 = (5 / 50) * 100 = 10%.

The coefficient of x^0 is (-4)^5 = -1024.

The coefficient of x^0 is C(3,0) * 5^3 = 1 * 125 = 125.

The coefficient of x^0 is C(5,0) * 5^5 = 1 * 3125 = 3125.

The coefficient of x^2 is C(4,2) * (3)^2 * (-4)^2 = 6 * 9 * 16 = 864.

Using the binomial theorem, the coefficient of x^2 in (a + b)^n is given by nCk * a^(n-k) * b^k. Here, n=6, a=x, b=-4, and k=2. Thus, the coefficient is 6C2 * (1)^4 * (-4)^2 = 15 * 16 = 240.

Using the binomial theorem, the coefficient of x^3 is given by C(5,3) * (2)^3 * (3)^(5-3) = 10 * 8 * 9 = 720.

The coefficient of x^4 is C(6,4) * (2)^4 * (3)^(6-4) = 15 * 16 * 9 = 2160.

The coefficient of x^4 is C(5, 4) * (2)^4 * (-3)^1 = 5 * 16 * (-3) = -240.

The coefficient of x^4 is C(6,4) = 15.

The coefficient of x^5 is C(10,5) * (1/2)^5 = 252 * 1/32 = 7.875.

The coefficient of x^5 is C(7,5)(2)^2 = 21 * 4 = 84.

The coefficient of x^5 is C(8,5) * (2)^3 = 56 * 8 = 448.

Using the binomial theorem, the coefficient of x^5 in (x + 3)^8 is given by 8C5 * (3)^3 = 56 * 27 = 1512.

The coefficient of x^6 is C(8,6) * (5)^2 = 28 * 25 = 700.

The complex ion [Cu(H2O)6]2+ is blue due to d-d transitions.

[Cu(H2O)6]2+ is known to exhibit a blue color due to d-d transitions in the presence of water ligands.

The combined gas law is represented by the equation P1V1/T1 = P2V2/T2, which combines Boyle's, Charles's, and Gay-Lussac's laws.

The common oxidation state of actinides in their compounds is +4.

Alkali metals have a common oxidation state of +1.