已 知平面流动的流速场为[tex=2.857x1.0]LOb0BBaSANRU53pQ7W0KhA==[/tex]，[tex=2.714x1.286]tfxrlk/BFndgIsh2WE9nrQ==[/tex]，其中[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]、[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]为常数，求流线方程并画出[tex=2.357x1.214]3RjJPcQqkZTXno6v4uVvlw==[/tex]时的流线。
举一反三
- 设[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex],[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]是整数且不全为0，而[tex=9.857x1.214]hhHzRVDsWGXE+Yltfe39hDUdsl3Yzf9jGRPDg4wYEoJYR6eBGAfms1GUG8a2PN1l[/tex]，证明[tex=0.571x1.0]TcM6B5Wrs5vy9dWrxRPSdg==[/tex]是[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]与[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]的一个最大公因数当且仅当[tex=4.214x1.357]jI1oqbiyUHYU1xbNvvBdDK5ib01K7Vb7AmVkL7RKEyk=[/tex]
- 求下列参数方程所确定的函数的导数[tex=1.357x2.429]S7luyuqBdxncyxDf4c61lQ==[/tex]:[tex=10.0x2.929]gu90YT9VhYiCoPhoSPPrwCOWL+2RzGu5DEZOkB60db72ulCfz5kSKXvoN6FsqcTPJ17OFAjGerY/5MFiOeARv1WizyRNRqt39kDuy9UQLbliWV2YBIxkttfOYEP+5qzW[/tex]([tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex],[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]为常数）
- 计算下述[tex=1.143x1.0]oTcZ8bPOd5+p8E1UHN7wXA==[/tex]阶行列式（主对角线上元素都是[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]，反对角线上元素都是[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]，空缺处的元素为0）：[tex=14.357x7.214]BafYOyQLkfv749f2fydiSmuFaORJrmT8ZJIXGdw44f1aEpC52UG/9KaK/rVnUNciUh3QoBqaPPxfmlIg/phge+h4iq0ABGDReZk1AL0sZKzKnThLESNQm78N48nK4v5O+GmV/flx/lbKKFGOzBOQhYxNt+leiRpulVjqMeOFBfnI0RXZdSR7MVvsUvgTHcf+ugGSltGkhpnoxUoJeFlxsZdoHZzCrpQrZ4mwb1kz/X/Fqe167F6aEL+T1v5e+y8WvVKhcL8g9UtTTbtwM8lNug==[/tex]
- 图9-26所示，金属球[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]和金属球壳[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]同心放置，它们原先都不带电。设球为[tex=0.857x1.0]6WwbFXETRyeyXlvAruSoNg==[/tex]，球壳[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]的内、外半径分别为[tex=0.857x1.0]BNzznGkXRFuGyw2vMy6rWw==[/tex]和[tex=0.857x1.0]Fz01PbYkU0SRGm3tB5KjiA==[/tex]。求在下列情况下[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]、[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]的电势差：使[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]带[tex=1.286x1.143]HtShgpkNmCs66SDQIt6cYg==[/tex],使[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]带[tex=1.286x1.143]NeILClIc8twxeO5vjYm8Dw==[/tex][img=203x220]17e1aa8f4234a38.png[/img]
- 求向量[tex=0.571x0.786]c59+3vo0/Vn/FvNRhDRu5g==[/tex]与[tex=0.429x1.0]JThLUuJ8WswSAPiYZWihWg==[/tex]的夹角：[tex=5.429x1.357]28vNNArDuRRnb+06piGt7g==[/tex]，[tex=6.143x1.357]Uqwu1QGYB2waFjV52ImPKg==[/tex] .