1 . 如图一,在平面直角坐标系
中,
为坐标原点,
,
,请根据以下信息,处理问题(1)和(2).信息一:
为坐标原点,
,若将
顺时针旋转
得到向量
,则
,且
;信息二:
与
的夹角记为
,
与
的夹角记为
,则
;信息三:
;信息四:
,叫二阶行列式.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/bf1df5da-7d9c-4f37-97ec-8360f768f8bf.png?resizew=306)
(1)求证:
,(外层“
”表示取绝对值);
(2)如图二,已知三点
,
,
,试用(1)中的结论求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47d5a819f2e82edbac8a82b05f64501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f68628a408537b1cf3bf1ca2a69731b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c02b54dc6b3e1bb6544f47d4c8743fcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/effc7768e61293768fcaf8c8979ff109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b9cffa9e859c54c97c1d58749f1993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36be470b9902a88939057d2f55280e55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d47d5a819f2e82edbac8a82b05f64501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774e4c61b6568d292d5bc576d3310d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b9cffa9e859c54c97c1d58749f1993.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/774e4c61b6568d292d5bc576d3310d8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad852a240fd16f5430472a3ff8c4063c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98afd2734ffaecbcb49e17416de7f062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d81a1c2ae937c87ee40f6b5d3e06bee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/bf1df5da-7d9c-4f37-97ec-8360f768f8bf.png?resizew=306)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b14e7b25d10dbe02750492faf9d0cd96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd483afbcdcd303e0c66ab48838bedfc.png)
(2)如图二,已知三点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773c2dd14d50e7f0d3326af4833d899a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5249114b149be585bc9b0fa1ae77e4ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed283a253b61df01f2a1cdc0cd8003f3.png)
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2020-08-03更新
|
220次组卷
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2卷引用:贵州省贵阳市2019-2020学年高一下学期期末考试数学试题
2 . 将4个数
,
,
,
排成2行2列,两边各加一条竖线记成
,定义
,上述记号就叫做2阶行列式若
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b29320f184b4027471a2951527457453.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9fec025453bac0d34d5e9bdf61a6755.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe09df62e1b245d7c7f5193707a826ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
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名校
3 . 关于x的不等式
的解集为
.
求实数a,b的值;
若
,
,且
为纯虚数,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/936cc21fdff36225c3107bd322b04077.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f3fd1e4a264b9c256df782129b4b312.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bf6c84731e5e1bd335ecfc2d36c3d81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f53190d6ead827a6338b9de847aeaf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/556b79148e57de2fbe66d0412eba1798.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce7c59bfeaca08f51ba8319f1098c36f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6da4e6752d8c8a0705194f2b2f16ab5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aef681e03396ab434adb3d28bd26150.png)
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2020-01-01更新
|
318次组卷
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6卷引用:7.3.2复数乘、除运算的三角表示及其几何意义(精讲)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)
(已下线)7.3.2复数乘、除运算的三角表示及其几何意义(精讲)-【精讲精练】2022-2023学年高一数学下学期同步精讲精练(人教A版2019必修第二册)上海市七宝中学2018-2019学年高三上学期摸底考试数学试题2016届上海市长宁区高三12月质量检测数学试题(已下线)模块09 矩阵和行列式初步-2022年高考数学一轮复习小题多维练(上海专用)上海市闵行区七宝中学2019-2020学年高三上学期开学考试数学试题(已下线)第02讲 不等式
4 . 若线性方程组的增广矩阵是
,解为
,则
的值为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fecf86370253119ccd5adc143382838.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d8ecea80af9b37ce7459030be16e0e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45aec1e4ca31a14444f4bc8682ab5d9f.png)
A.1 | B.2 | C.3 | D.4 |
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5 . 若复数
满足
,其中
是虚数单位,则
的虚部为________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81e59019989b7dc2fb59b037ef6e010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/006c521d2af43ef61f2dcaacb5382e6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7035cd4adda5d72a9fc9f9fda75995.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66e9585a1da28d403536ea48b4c37a3e.png)
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2019-11-09更新
|
441次组卷
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8卷引用:专题2.4 复数【专项训练】-2020-2021学年高一数学下学期期末专项复习(沪教版2020)
(已下线)专题2.4 复数【专项训练】-2020-2021学年高一数学下学期期末专项复习(沪教版2020)上海市建平中学2018-2019学年高三上学期12月月考数学试题上海市建平中学2019-2020学年高三上学期10月月考数学试题2020届上海市高三下学期高考预测数学试题(已下线)热点05 数列与不等式-2021年高考数学【热点·重点·难点】专练(上海专用)(已下线)热点04 平面向量、复数-2021年高考数学【热点·重点·难点】专练(上海专用)上海市复旦大学附属中学2020-2021学年高二上学期期末数学试题上海市致远高级中学2020-2021学年高二上学期期末数学试题
6 . 已知
(
为常数),
,且当
时,总有![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8162bee503aecf1dd7f835635b63bd.png)
,则实数
的取值范围是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60cf9ee8dde338b022a4366c5dcd59bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e4e360b821890b2afdcbc32a0fa0b85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f58620b99bef329c27333ec461234ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8162bee503aecf1dd7f835635b63bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3ec8f79b42db17aff3a207f371156ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2020-01-10更新
|
187次组卷
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4卷引用:第3章 函数-【优化数学】单元测试能力卷(人教B版2019)
(已下线)第3章 函数-【优化数学】单元测试能力卷(人教B版2019)上海市黄浦区2016-2017学年高三上学期期终调研测试数学试题2017年上海市黄浦区高考一模数学试题(已下线)模块09 矩阵和行列式初步-2022年高考数学一轮复习小题多维练(上海专用)
7 . 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
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9卷引用:【新教材精创】12.2 复数的运算 练习
(已下线)【新教材精创】12.2 复数的运算 练习第五章 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
8 . 已知
=
是矩阵M=
属于特征值λ1=2的一个特征向量.
(Ⅰ)求矩阵M;
(Ⅱ)若
,求M10a.
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908679688192/1571908685438976/STEM/36af06dc9e6b45658ac244111813be00.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908679688192/1571908685438976/STEM/cbc01f7080bf452297948908a4bd8079.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908679688192/1571908685438976/STEM/491d4d91de984a94990224df77d37d42.png)
(Ⅰ)求矩阵M;
(Ⅱ)若
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908679688192/1571908685438976/STEM/c18bee516d374a4abfac5e0ca18607f2.png)
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9 . 给定矩阵
,
;求A4B.
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908679688192/1571908685389824/STEM/80551eed0b3c4c418264fcef7c08603f.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908679688192/1571908685389824/STEM/91f6b8b7cfec430e8aa3110db68e7270.png)
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13-14高一·全国·课后作业
10 . 已知矩阵A=
,向量
=
.求向量
,使得A2
=
.
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908478935040/1571908484694016/STEM/a8d5ec7e5b8443d792b12f73c3586926.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908478935040/1571908484694016/STEM/510be974f37643128ce60275d893846e.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908478935040/1571908484694016/STEM/7aac76233bc44a9d939fcd01bfa78ac4.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908478935040/1571908484694016/STEM/6c34684172be446494ad6d05bcdab1ea.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908478935040/1571908484694016/STEM/6c34684172be446494ad6d05bcdab1ea.png)
![](https://img.xkw.com/dksih/QBM/2014/12/2/1571908478935040/1571908484694016/STEM/510be974f37643128ce60275d893846e.png)
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