1.The car passed through the streets ( )we thought was a ver

解析如下：
1.因为从句与“the street”构不成修饰关系,所以从句不是定语从句.
故A,B选项排除,又因主句不缺主干成分,无法接what引导的名词从句故D选项排除.选项C at what 是介宾短语作主句状语.what本身引导一个名词从句来表述
以一种什么样的速度
补充:
Speed 作名词的用法
(1)at + full/top/low/a high/an ordinary/the same + speed
以全（高、低、高、平常、同样)的速度
(2)"at a speed of..." 以……的速度
at a speed of 700 miles an hour
at a speed of 160m/s.
The car passed through the streets we thought was a very dengerous speed.
全句译：这个汽车以我们认为非常危险的速度穿过街道.
2.This hospital is ___you once worked for 10 years?
还原成陈述句清楚可见主句缺表语,故排除B,C.因为关系代词没有可修饰的先行词,A选项虽可做主句的表语,但又缺少引导从句的关系词.排除.
Is this hospital you once worked for 10 years?
这家医院是你曾经工作十年的地方吗?
the one 作先行词,where 替代先行词在定语从句中做地点状语等于at this hospital.
If you still feel confused ,leave a message please!