Which ones are vector fields? (I checked my answers)
Temperature of room at given point
The gravitation that object with mass creates (x)
The density of an object at given point
Function $f: \Bbb{R}^3\to\Bbb{R}^3 $ (x)
Function $f: \Bbb{R}^3\to\Bbb{R} $
Gradient of function $f: \Bbb{R}^3\to\Bbb{R}$ (x)
Derivate of function $f: \Bbb{R}\to\Bbb{R} $
Speed of a water molecule in a river
Function $f: \Bbb{R}^2\to\Bbb{R}^2 $ (x)
Function $f: \Bbb{R}^2\to\Bbb{R} $
Tangent of a circle at given point
Did I got them right?
No, temperature is a scalar, and so is density! Those are both what are known as "scalar fields." Also, speed is a scalar.
The gradient is also a vector field!