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解题方法
1 . 已知向量
,
是坐标原点,若
,且
方向是沿
的方向绕着
点按逆时针方向旋转
角得到的,则称
经过一次
变换得到
,现有向量
经过一次
变换后得到
,
经过一次
变换后得到
,…,如此下去,
经过一次
变换后得到
,设
,
,
,则
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac66b00e6cb8d30f293f3baeb501333e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb9307fa2c34a86800d60a194747a788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d60dcb171bb7fd972aab8294d63acdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52831e39d2f23629c6699103ff5d1d67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f66c2415abe65e3fab5574c08d8d1e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bc22dd6172821ef009d031d466bdd3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7559d65befe0b85c8929f57c9436cd26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7559d65befe0b85c8929f57c9436cd26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1cd05a7d73db8c7a63ba8e3854ef259.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c81c88f84b0533f32d4008a5088b21cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79d7c41caf47f014d2158abe25a876ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45acb8f1484640eef1f6439be92f1a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07d8b2f1f9ead1e148c04fb2538421e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4c7fc2ab3dc022658351fd10a5e07b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4799f1244959c9118346ced85adc4197.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449259bdbfccf519730ad5a0522d80f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3677f2a2a1b4aef3a370a03db832366.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2 . 将曲线
按照伸缩变换
后得到的曲线方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b80edc0756f43ca971a3d0a3cdb747e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550cd747db6dad5c19dd728e9381952d.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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3 . 矩阵的一种运算
,该运算的几何意义为平面上的点
在矩阵
作用下变换成点
,若曲线
,在矩阵
的作用下变换成曲线
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c158a0dafc1ed72d4cd92ce8be537d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1eaadd274b7644891f5550a799a11bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe027ff8bff5b84819a7d2c514e9de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3fa06df195ae83f7ea63b16158748be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5339be0bc4d6f090b6de7112636d500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760a793ad8dadeba59aef81106e95288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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真题
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4 . 某班试用电子投票系统选举班干部候选人,全班k名同学都有选举权和被选举权,他们的编号分别为1,2,
,k,规定:同意按“1”,不同意(含弃权)按0”,令
,其中
,且
,则同时同意第1,2号同学当选的人数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa5e9bd516f6282483b92cfe6074623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/237e6478ccb922c911926fc7fe2c1954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/940cd957b9db25326a0c7a413df7f1d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d796f419d4ef9ba590cb825ebb87cdd4.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
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2022-11-09更新
|
233次组卷
|
6卷引用:2003年普通高等学校招生考试数学(理)试题(北京卷)
2003年普通高等学校招生考试数学(理)试题(北京卷)2003年普通高等学校招生考试数学(文)试题(北京卷)2019年上海市上海中学高三下学期数学测试2数学试题(已下线)考向16 数列求和及数列的综合应用-备战2022年高考数学一轮复习考点微专题(上海专用)北京一零一中学2020-2021学年高一新生入学摸底测试数学试题辽宁省实验中学2023-2024学年高二下学期期中阶段测试数学试卷
5 . 以下能成为以行列式形式表示的直线方程
的一个法向量的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f25d23d0f767500f07f841de759934.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 定义运算
,则符合条件
的复数
为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ffd664f7aca7c3e36eca887dab7bce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a14261bf16490f05ad8c3794d765f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2016-12-04更新
|
854次组卷
|
9卷引用:2014-2015学年山东省华侨中学高二4月月考理科数学试卷
2014-2015学年山东省华侨中学高二4月月考理科数学试卷2015-2016学年内蒙古准格尔旗世纪中学高二下第一次月考理科数学卷湖北省部分重点高中2019-2020学年高三11月期中联考数学理科试题甘肃省庆阳市宁县第二中学2019-2020高二下学期4月线上测试数学(理)试题江西省宜春市上高县第二中学2019-2020学年高二(6月)第二次月考数学(理)试题(已下线)【新教材精创】12.2 复数的运算 练习山西省怀仁市2020-2021学年高二下学期期中数学(文)试题江西省抚州市南城县第二中学2021-2022学年高二下学期第二次(月考)数学(理)试题第五章 复数章末检测卷-2021-2022学年高一下学期数学北师大版(2019)必修第二册
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7 . 关于
的方程组
的系数矩阵记为
,且该方程组存在非零解,若存在三阶矩阵
,使得
,(0表示零矩阵,即所有元素均为0的矩阵;矩阵
对应的行列式为
),则
(1)
一定为1;
(2)
一定为0;
(3)该方程组一定有无穷多解.
其中正确说法的个数是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b8ec9d4206ea66a02de5c4a1e1e911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/726b31b9e4f085fb2754723f21405d86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d52399e72456de84f0a42dd69da06fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93499d2c5181db3ef5db16b64c2a4911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8f054b30b493c4ce1deecff3468c08.png)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc8f054b30b493c4ce1deecff3468c08.png)
(3)该方程组一定有无穷多解.
其中正确说法的个数是( )
A.0 | B.1 | C.2 | D.3 |
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8 . 若矩阵
,记
,以下四个命题中的矩阵
都是
阶矩阵,
,则其中真命题的个数为( )
① 若
,则
; ② 若
,则
;
③
; ④ 若
,则
;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10a63c1c60b695b37bec52bfb8bae214.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e81d3ab9b33676f3f04bdd34449f68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b72fcdc709e77910cd36a26369648b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e5d6bebc33fde49c8b270b1887de4a5.png)
① 若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bd9736828195f010db4e1f0a9dea7a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d84d34bdf10cf4772eaa806f2095347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12817ef243b1be51a55dba0d247c166f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0c8af715d1ac1da11c83d2e2997da2a.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bbe7feba91e145df12b2d484519846b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3919e463a93ac597ca35c0e3bc000565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92a582a1144cde44ce324cb9f1e94b4.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . 矩阵的一种运算
,该运算的几何意义为平面上的点
在矩阵
作用下变换成点
,若曲线
,在矩阵
的作用下变换成曲线
,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c158a0dafc1ed72d4cd92ce8be537d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1eaadd274b7644891f5550a799a11bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f989e3dc5d752aa2638069f325807db0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb99abc26156c2dfe6941041e7e9f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5339be0bc4d6f090b6de7112636d500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/760a793ad8dadeba59aef81106e95288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20d6fc9b90f370fbb27552876b650f8f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2019-12-14更新
|
200次组卷
|
2卷引用:2018年上海市复旦附中高三5月三模数学试题
10 . 对于集合A,定义了一种运算“
”,使得集合A中的元素间满足条件:如果存在元素
,使得对任意
,都有
,则称元素e是集合A对运算“
”的单位元素.例如:
,运算“
”为普通乘法;存在
,使得对任意
,都有
,所以元素1是集合R对普通乘法的单位元素.下面给出三个集合及相应的运算“
”:
①
,运算“
”为普通减法;
②
,运算“
”为矩阵加法;
③
(其中M是任意非空集合),运算“
”为求两个集合的交集.
其中对运算“
”有单位元素的集合序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c857a4984543f15c4637084f0e0db0d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cc020b0997a2f37b214718112b79d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c88aa4c16567c4cfda0fe4df69751a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843c3f388a75bf981c11ca947a86e5fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d15b0b4873f8b9320f22437525bc96f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/845198de78fd8737a5bce7178622ca36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/843c3f388a75bf981c11ca947a86e5fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24c01a4595d9129a944090973728205a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8a4e50298e5cc496e0d4e00d84403ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
其中对运算“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c3c2f679d53b91088ba6eb14c16cbc0.png)
A.①② | B.①③ | C.①②③ | D.②③ |
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2015-01-28更新
|
746次组卷
|
6卷引用:2015届上海市闸北区高三上学期期末练习理科数学试卷
2015届上海市闸北区高三上学期期末练习理科数学试卷2015届上海市闸北区高三上学期期末练习文科数学试卷上海市静安区2017-2018学年度第一学期高中教学质量检测高三数学试卷上海市复旦大学附属中学2019届高三高考4月模拟试卷数学试题(已下线)第1章《集合》 培优测试卷(一)-2021-2022学年高一数学上册同步培优训练系列(苏教版2019)(已下线)课时28 矩阵的概念及运算-2022年高考数学一轮复习小题多维练(上海专用)