This seems more like a math question to me (I've only seen it in functional analysis), but anyway. In this (and most cases), \Subset tends to be used as an alternative to (the in my opinion rather ugly) \subset\subset, and means that one set is compactly contained (or embedded) in the other. For...
You do realize that physics is all about coming up with these rules to describe and predict the way the world behaves, right? That is the scientific way. Usually the rules take the form of equations (though it's not obvious a priori why mathematics should be useful at all). Sometimes we can...
I think, at least in some models, the antenna itself is rotating. Whether that is better or not, I don't know - still using a turntable variant here. Though it seems that these models are very hit or miss, so make sure to read the reviews on that specific microwave first.
In physics, the word 'field' basically indicates some (scalar-, vector-, operator- or whatever-valued) function that is defined on some space (usually three-dimensional Euclidean space or 4D Minkowski spacetime), rather than a set with two operations (that satisfies some additional properties)...
Acceleration as the time derivative of velocity? Yeah, that should work (and how could you make it shorter?), but velocity is a vector so \vec{a} = \dot{\vec{v}}, or in the Leibniz notation,
\vec{a}=\frac{d\vec{v}}{dt}
Certainly! I'm not advocating that you should account for everything in calculations, but I am advocating to keep in mind that our simple models of physics aren't the whole truth.
One way of thinking of things may be advantageous for calculations, another less so. The first way doesn't even...
I'm curious, is there any natural or intuitive way to think of dispersion in this picture? Why should blue light need a different number of bounces than red light, for example?
The advantage is that you don't have to explain how the light accelerates to c after leaving the medium...
That is true in vacuum, but not in media. In a medium, different wavelengths travel at different speeds (this is called dispersion), so different wavelengths get different refractive indices. This is why a prism splits white light into different colors, for example.
Nothing special about the head, really. You lose heat from any exposed part of the body. It's just that we tend to cover the other parts of the body before considering donning a hat.
From the British Medical Journal 2008;337:a2769:
Doesn't the insulating effect mainly come from the layers of air between the blankets and pockets of air inside the blankets? In that case, the heavier blankets would compress the lower, lighter blankets and provide less insulation. On the other hand, the thicker blankets probably breaks airflow...
Well, it all boils down to symmetries (Noether's theorem), but there doesn't seem to be a good systematic way to find all symmetries of a given Lagrangian. In fact, some symmetries are really hard to find in a given coordinate system. Translational symmetries (associated with momentum...
The choice of the units you consider fundamental should depend on the practical accuracies as well. Well, at least if you want to use them for measuring things and deriving other units. Post #53 in https://www.physicsforums.com/showthread.php?t=418112&page=4 has a bit on this when it comes to...
http://en.wikipedia.org/wiki/Standard_conditions_for_temperature_and_pressure
It's a jungle of standards really. To have any idea, see if the conditions are stated elsewhere in the publication or hand, or make your best guess from the wiki article.
The same should be true for hydrogen, shouldn't it? On the other hand there's some ten times as much helium, so He probably dominates the atmospheric escape.
Yes, the material is cut using the laser beam. Light only. The used lasers are high power gas lasers. Also see http://en.wikipedia.org/wiki/Laser_cutting
To keep up the high power output you need a rather pure gas atmosphere. Sadly you can't just seal the resonator tube and let it be, because...