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Тест по геометрии для 9 класса на тему "Сложение и вычитание векторов"
Даны векторы A = (3, 4) и B = (1, -2). Найдите вектор C, который равен их сумме: C = A + B.
Ответ:
C = (3 + 1, 4 - 2) = (4, 2).
Даны векторы D = (-2, 5) и E = (3, 1). Найдите вектор F, который равен разности векторов: F = D - E.
Ответ:
F = (-2 - 3, 5 - 1) = (-5, 4).
Если векторы G = (x, 2) и H = (3, y) такие, что их сумма равна I = (5, 6), найдите значения x и y.
Ответ:
x + 3 = 5 ⇒ x = 2
2 + y = 6 ⇒ y = 4.
Таким образом, x = 2 и y = 4.
В данном контексте, векторы J = (2, -1) и K = (5, 4). Определите вектор L, который находится на одной трети от вектора J и на две трети от вектора K: L = (1/3)J + (2/3)K.
Ответ:
L = (1/3 * 2 + 2/3 * 5, 1/3 * (-1) + 2/3 * 4) = (2/3 + 10/3, -1/3 + 8/3) = (12/3, 7/3) = (4, 7/3).
Векторы M и N имеют координаты M = (a, b) и N = (c, d), где a = 1 + 2b, c = 3 - d. Найдите вектор P = M - N, если b = 2 и d = 1.
Ответ:
Находим a и c:
a = 1 + 2*2 = 5,
c = 3 - 1 = 2.
Теперь вычисляем P:
P = (5, 2) - (2, 1) = (5 - 2, 2 - 1) = (3, 1).
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Ниже тест по английскому языку. Тема: описание внешности человека. Класс: 4-й. Тип вопросов: Единственный выбор. Количество вопросов: 10. Выводится без ответов.
Which sentence describes a person who is tall? A) He is tall. B) He is short. C) He has long hair. D) He wears a hat.
Which sentence describes someone with blonde hair? A) He has brown hair. B) She has blue eyes. C) She has blonde hair. D) He has red hair.
Which sentence describes someone with blue eyes? A) She has blue eyes. B) She has brown eyes. C) She has green eyes. D) He has violet eyes.
Which sentence describes someone with long hair? A) He has short hair. B) She has long hair. C) He has bald head. D) She has no hair.
Which sentence describes someone with curly hair? A) She has straight hair. B) He has curly hair. C) He has thin hair. D) She has no hair.
Which sentence describes someone who wears glasses? A) He wears glasses. B) He wears a scarf. C) He wears a hat. D) He wears a belt.
Which sentence describes someone wearing a blue shirt? A) She wears a blue shirt. B) She wears a red shirt. C) She wears a green shirt. D) She wears a yellow shirt.
Which sentence describes someone with a round face? A) He has a round face. B) He has a square face. C) He has a long face. D) He has a narrow face.
Which sentence correctly describes someone with short hair? A) He has short hair. B) He has long hair. C) He has curly hair. D) He has missing hair.
Which sentence describes someone with brown hair and green eyes? A) He has brown hair and green eyes. B) He has brown hair and blue eyes. C) He has blonde hair and green eyes. D) He has black hair and brown eyes.
Решите неравенство:
(\log_2(x - 3) > 1)
Решите неравенство:
(\log_{10}(2x + 1) \leq 0)
Решите неравенство:
(\log_5(x + 4) - \log_5(x - 2) < 1)
Решите неравенство:
(\log(3x - 5) \geq 1)
Решите неравенство:
(\log_3(x^2 - 1) < 2)
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Инструкция: Заполните пропуски подходящими формами глаголов в Present Simple или Present Perfect.