"Presumably they negotiate the payment they want so they don't need to go shopping later. I was never offered payment, or an opportunity to turn this down." She perks up. "Can I sue the tower's owner for kidnapping?"
"We have scientists studying magic and engineers (*) making our magic items," (casting implements has no specific translation) "but I don't know how far they'd get with written instructions from a completely different tradition, not only of magic but of other physical sciences. I'll buy a copy of any reference and encyclopedic works I can find, but they'd need to be in some compact form, I can't carry a library in my backpack... At least the reading problem is solvable, and the magic hat itself could be valuable to study."
"My world's magic can do - almost any physical effect, in theory, and new spells keep being invented or refined. There are hundreds, probably thousands, of spells used in industrial chemistry and manufacture. I don't know about most of them, and it's a rapidly developing field. The spells I have are those useful to a military aerial mage in our current doctrine. Weapons and shields aside, I can fly - ceiling of twelve thousand feet, though it's tiring to stay higher than eight, and with a maximum speed of eight hundred - um." Her knowledge of Osiriani is informing her that it has a word for 'foot' but not 'meter' or 'second'. They must use a different-length foot, too, it's good she caught herself. "This is a meter" (she shows one in an illusion). "I can fly at an altitude of 2400 meters, up to 3600 in emergencies. And a maximum speed of 220 meters per this time unit." Illusion of a one-second metronome. "The speed limit is due to drag, I spend more power the faster I'm flying."
"I can make illusions, as you've seen. If they're of things I'm imagining then they're limited by my ability to visualize, but I can also record what I'm seeing in the moment and reproduce it later more exactly than my own memory would allow. Aerial mages were originally used as observers; to that end I have an optical magnification spell" - she makes a small one to demonstrate - "up to a thousand-fold magnification. To benefit from that much you need good visibility conditions, of course. And know where to aim it; if a target isn't itself using detectable magic, I don't have any spells that would let me find it. This might be useful for mapping or some other aerial observation, if you haven't solved that class of problems yet. It can also be used as an optical microscope."
"Aside from that, I can produce directional light stronger than an illusion, make mirrors... The light can be -" no word for infrared?? "an emission of invisible heat, I can't find the right word for some reason..." What else. Her so-called speed-up spells (drugs synthesized and decomposed by magic directly in her brain) can't be used on other people, or at least she doesn't know how to make the orb do that. "I have a weak healing spell for emergencies, it speeds up natural healing and helps disinfect wounds. I have a short-range radio unit. You don't seem to be using radio transmissions, is it all magical communications or something else? Ah, I'm sorry, radio is signalling via the same force as light and heat but even longer waves than heat. I don't know the technical terms in this language." Did she get a defective translation spell or do these people have a completely different theory of physics? Magic detection is presumably not useful, she can't do any actual analysis on their unfamiliar spells and her orb can't compete with a proper magic radar (†) anyway.
"Outside magic and the military, I have experience as a human resources manager, but I can't imagine working here without a lot of retraining. It depends intimately on company culture - and actual culture - and on the relevant laws. Having since commanded military units of up to a thousand people, I'm afraid management technique does not generalize well across different kinds of organizations."
Honestly, if any of Tanya's magic abilities is competitive here, the best way to capitalize on that would be to teach more people to make and use Earth-style casting implements. Even if her particular spells aren't valuable, the overall technology might be. But she's not in the least qualified to do that, and reverse engineering her orb - would be very difficult on Earth but she has no idea how to judge it here, which is another reason not to mention the possibility right away! And she doesn't know what kind of attention she might draw to herself. If computation orbs turn out to be anywhere near as groundbreaking as they were on Earth they would make her subject to geopolitics, and she does not need that kind of excitement in her life.
(*) Incredibly smart. Also, make things and people explode in the name of progress. Sadly, Osiriani does not seem to have a word for 'mad scientist/engineer' other than mages and chemists.
(†) So-called by analogy with normal radars, these large ground-based detection units are in fact passive. However, they use magic for their own operation, which allows them to be detected and targeted.