A. Trong mặt phẳng Oxy , phép quay mỗi vector quanh gốc tọa độ một góc  ngược chiều kim đồng hồ là một ánh xạ tuyến tính (Hình 1). Hãy tìm ma trận biểu diễn và biểu thức của phép quay trên. Áp dụng: Cho tam giác MNP gồm các

đỉnh M(1,1) ,

N(1, 2) , P(3, 3)

hãy tìm ảnh của

tam giác MNP qua phép quay nói trên, biết

góc quay là    / 4

và vẽ hình biểu diễn.

b. Trình bày một ứng dụng của môn học này.

In factoring by grouping, what would you have for step 3 for the following? step 1: x^3 +5x^2 +4x+20 step 2: x^2 (x+5)+4(x+5) step 3: ?

Find the distance between c and d on the number line c=3 and d=11

Submarines control how much they float or sink in the ocean by changing the volume of air and water contained in large ballast tanks. when the tanks are completely full of water, the submarine increases its overall mass and sinks down to the bottom. when the tanks are completely full of air, the submarine reduces its overall mass and floats to the surface. depending on the density of the seawater surrounding the submarine, it will pump seawater in or out of the tanks in order to achieve the same overall density as the sea water and float neutrally in the water. the volume of the submarine never changes. when the tanks are completely full of water, a submarine with a volume of 7.8\times10^3\text{ m}^37.8×10 3 m 3 7, point, 8, times, 10, start superscript, 3, end superscript, space, m, start superscript, 3, end superscript has a total mass of 8\times10^6\text{ kg}8×10 6 kg8, times, 10, start superscript, 6, end superscript, space, k, g. the density of the seawater is 10^3\text{ kg/m}^310 3 kg/m 3 10, start superscript, 3, end superscript, space, k, g, slash, m, start superscript, 3, end superscript. to make that submarine float neutrally, and neither float nor sink in the ocean, what volume of water does that submarine need to subtract from its tanks?